Sedimentation Paper

Analysis of the Effect of Slurry Concentration and Height on Sedimentation Characteristics of Kaolin-Water Mixture D.S. Corpuz, J.L. de Guzman and J.M. Golbin Department of Chemical Engineering, University of the Philippines-Diliman, Quezon City, Philippines

D.S. Corpuz, J.L. de Guzman and J.M. Golbin, 2008. Theoretical discussions predict that initial slurry concentration and height affect the sedimentation characteristics, particularly settling time and settling velocity. From experimental data, it was shown that the settling velocity of a mixture decreases with increasing concentration, yet reverses trend in the compression settling zone; and settling time needed to reach the final height increases with increasing initial slurry height. Keywords: compression settling, critical settling point, drag force, free settling, hindered settling, rate-limiting layer Stokes Law, terminal velocity OBJECTIVES The experiment aimed to observe the relationship of settling time with slurry concentration, as well as with initial slurry height. This experiment also intended to determine the behavior of settling velocity as the sedimentation process proceeds. The effect of slurry concentration with particle settling velocity was also studied. THEORETICAL BACKGROUND Sedimentation is one of the methods used in industry to separate liquid-liquid or solid-liquid mixtures. By definition, sedimentation is the separation of a dilute slurry or suspension by gravity settling into a clear fluid and a slurry of higher solids content (Geankoplis, 1993). The resulting liquid is essentially particle free. In industry, either the particle free liquid or the particles itself is the desired product. Basically, sedimentation is the movement of particles through a fluid. All throughout its motion, three forces act on the particle, namely, buoyant force, gravitational force, and drag force (Geankoplis, 1993). Buoyant force, Fb, is the upward force exerted by the fluid on the particle, and is given by the equation

where m/ρp is the volume of the particle, ρ is the density of the liquid, and g is the gravitational constant. The gravitational force, Fg, on the particle is given by Newton’s Law as The drag force, FD, is the frictional resistance related to the velocity head of the fluid displaced by the moving body (Geankoplis, 1993) and is given by the equation

where CD is the dimensionless drag coefficient, and is velocity head. The drag coefficient is a function of the Reynolds number. In the laminar flow region where NRe<1, Stokes’ Law dominates and CD is given by (Geankoplis, 1993) (1) In sedimentation, the particles experience a period of accelerated fall and a period of constant velocity fall (Geankoplis, 1993). The constant velocity period is usually of more importance, as the accelerated fall period is very short relative to the constant velocity period. In the constant rate period, the particles reach a maximum settling velocity known as the terminal velocity, vt. The terminal velocity is determined by solving the velocity at which the sum of the three forces is equal to zero. Geankoplis gives the equation for the terminal velocity of spheres as (2) where Dp is the particle diameter.

Equation 2 gives the terminal velocity for free settling wherein a particle is at a sufficient distance away from the wall and other particles (Geankoplis, 1993). In general, however, particles experience hindered settling, that is, the velocity gradients around each particle are affected by the presence of nearby particles (McCabe, 2001). The drag force in hindered settling is greater than in free settling because of the interference of the other particles, thus the settling velocity for hindered settling is less than that for free settling. (Geankoplis, 1993) The terminal velocity becomes a function of ε, the volume fraction of the slurry mixture occupied by the liquid. Several correlations have been developed to analyze settling velocity for hindered settling, and their methods and derivations are beyond the scope of this experiment. PROCEDURE The experiment involves the analysis of the effect of varying the height of the slurry and their concentrations on the sedimentation properties. To determine the effect of initial slurry height on sedimentation properties, three samples with the same concentration of 2.5% kaolin-water solution were made. Initial slurry of 800 mm, 600 mm and 400 mm were assigned. The slurry inside the vessel was ensured to have a homogenous characteristic by rigorously mixing and shaking the sedimentation cylinders. Starting at the same, the mixtures were allowed to settle, and at intervals of 2 minutes, the heights of the clear regions of the three samples were recorded. Total observation time was 2 hours. For the second part of the experiment, the effect of concentration on the sedimentation properties was analyzed. The volume (or height) of three new samples was made constant, and their concentrations are varied (2.5%, 5%, 7.5%). The heights of the clear regions were recorded with intervals of 2 minutes for the first two hours. The samples were left overnight and the last point was to be recorded at that period. For this experiment’s case, more than twenty-four hours was observed.

RESULT AND ANALYSIS

Clear liquid interface height, z, cm

The mechanism of solid settling from slurry can be best observed in a glass cylinder as shown in Fig. 1 below.

Clear Liquid Interface vs. Settling Time (Varying Initial Heights)

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Fig. 2. Clear Liquid Interface vs. Settling Time (same concentration, different initial heights)

Fig.1 . Batch Sedimentation (Source: McCabe, 2001)

One of the objectives of this experiment is to determine the effect of varying initial slurry heights (or volume) on the sedimentation characteristics. Initially, the concentrations of the three samples were kept constant and their initial height was varied. The results for the first objective are presented first, followed by the results for the varying concentration.

As discussed earlier and shown in Fig. 1, different zones appear during sedimentation. Fig. 2 is a plot of the depth of the clear zone versus time. The plot shows that during initial stages of sedimentation, the depth of the clear zone decreases at a constant rate as sedimentation goes along, as shown by the steep linear part of the plot. The plot also shows that the slope changes after a certain depth has been reached. The curve of the plot during the later stages of sedimentation is almost horizontal yet still almost linear. The part of the plot that is almost horizontal represents the compression settling stage, wherein hindered settling dominates.

Fig. 3. Getting the zone settling velocity (Source: www.ceeserver.cee.cornell.edu)

As shown by Fig. 3, the settling velocity for the different regions can be determined from the plot of liquid interface height versus time. The slope of the steady interface subsidence rate represents zone settling velocity. Tube 1: Determination of Velocity 900 800

Clear liquid interface height

Initially, the slurry is uniformly concentrated and the initial height is zo, as shown in Fig. 1a. The concentration of the slurry is high enough that the particles affect each other’s rate of fall to the extent that after a short time, all particles settle at the same velocity and are assumed to approach rapidly the terminal velocities under hindered-settling conditions (Foust, 1980). The concentration is high enough to cause settling as a matrix, that is, the particles remain in a fixed position relative to each other as they settle (www.cee.cornell.edu). Heavier solids settle faster, thus forming zone D shown in Fig. 1b. Zone A is the region of clear liquid (Foust, 1980). Zone B is a region of uniform concentration which is essentially equal to the initial slurry concentration (McCabe, 2001). In this zone, the particles settle by free settling and at a uniform rate (Geankoplis, 1993). Zone C is the transition region wherein the concentration is nonuniform and the sizes of the particles are varied (Foust, 1980). As sedimentation goes on, the depth of zone B decreases, the depths of zone A and D increase, while that of zone C remains constant, as shown in Fig. 1c (McCabe, 2001). Zone B eventually disappears, and the solids in zone C and D merge such that only zone D is distinct, as shown in Fig. 1d. During this stage, the matrix of particles gets constrained from the bottom because of the bottom of the settling tank. Such a situation is called compression settling (www.cee.cornell.edu). The moment (or height) at which zone B and C disappear and all the solids appear in zone D is referred to as the critical settling point. By definition, it is the point at which a single distinct interface forms between the clear liquid and sediment (Foust, 1980). Beyond the critical settling point, sedimentation occurs by compression. The gradual accumulation of the upper particles compress the solids at the bottom and decrease the height of zone D, and force the residual liquid in zone D out upward through the solids into the clear liquid zone. The settling rates during compression settling are very slow, and the rates may be estimated using hindered settling computation methods. Fig. 1e shows the end state of the sedimentation process, in which the weight of the solid is balanced by the compressive strength (McCabe, 2001). Sedimentation design and calculations are based upon identifying the concentration of the layer having the lowest capacity for the passage of solids through it. This particular layer is called the rate-limiting layer, cL (Foust, 1980).

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Fig. 4. Determining the settling velocity

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From the y-intercept of the tangent lines in Fig. 4, the height zi that the slurry would occupy at concentration cL is determined. The zi data can be used to determine the minimum concentration cL at which boundary layer interferes, using the equation (4) where co and zo are the initial concentration and height, respectively. Exact values of cL are given in the appendix. Settling velocity vs. Concentration

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the nearer presence of the other particles slow each other’s settling velocity. The velocity in the compression settling zone is significantly less than that in the earlier region. Fig. 5 also shows how the initial height (or volume) of the mixture affects the settling velocity of the mixture. The sample with the highest initial height (namely, tube 1) had, in general, the fastest settling rates compared to rates of the other samples.

Tube 1: Height vs. Time 900

Clear liquid interace height, z, cm

Fig. 4 shows the method used in this experiment to determine the settling velocities at different points. The slopes of the tangent lines at each point, which is equal to the settling velocity at the point, were determined. In equation, (3) The exact values of the settling velocities of each trial are shown in the appendix.

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Settling time, θ, hrs

120

Fig. 7. Getting the critical settling point

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Concentartion (g/L) tube 2

tube 3

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Fig. 5. Settling Velocity vs. Concentration (same height, different concentration)

As the sedimentation process goes along, the concentration of the solids region increasingly becomes more concentrated because the solids are getting more compacted. As this happens, the settling velocity decreases as the concentration increases, as shown in Fig. 5. Notice that the velocity decreases at almost a constant rate when the concentration is relatively low. Settling Velocity vs. Settling Time

Additional information that can be determined from the z vs. θ plot is the critical settling point, as illustrated in Fig. 7. The critical point is the point where a single distinct interface forms between the clear liquid and sediment can be obtained. At the start of sedimentation, the solids have a concentration co and free settling is observed. A tangent line is drawn at this part. On the other hand, another linear behavior which is almost horizontal is observed at the other end of the graph. A tangent line is also drawn at this part. These lines are extended until they intersect. The angle between these two lines is measured and an angle bisector is used. The bisector is extended until it touches the curve. The point of intersection is the critical point. A tangent line is made at the critical point. Extending this line gives the value of the concentration and time at the critical point. (Foust, 1980) Time to Critical Point vs. Initial Height Time, mins

Settling Velocity (cm/hr)

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Settling velocity, vt, cm/hr

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Initial Height, mm tube 1

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Fig. 8. Time needed to reach critical point vs. Initial height

From Fig. 8, it is observed that the sample with the highest volume (or height) takes longer to reach its critical point. The main reason for this phenomenon is that the time to reach the critical point would be influenced by the amount of sediment that has to settle as it reaches the critical point. Generally, this is the only effect of varying the height of the slurry can have. Initial height doesn’t necessarily affect the sedimentation rate.

Settling Time, θ, hr

Fig. 6. Settling Velocity vs. Settling Time (same concentration, different initial heights)

Fig. 6 shows the trend of settling velocity as sedimentation goes along. It should be noted that there are regions wherein the velocity is approximately constant. The settling velocity also experiences significant change. It can be seen that the velocity decreases as the sedimentation goes along, as is theoretically expected. This is because the hindered settling region is increasingly becoming more concentrated as time goes on and

For the second part of the experiment, the objective was to determine the effect of initial concentration on sedimentation characteristics. Three samples of kaolin-water slurry were made with different concentration. It is expected that the rate of descent of the solid-liquid interface is a function of local concentration (Foust, 1980).

settling zone. The settling velocity used in Fig. 11 was computed using the method illustrated in Fig. 4.

Height vs. Settling Time (Varying Initial Concentrations) 100

It should be noted from Fig. 6 and Fig. 11 that the zone settling velocity depends more on the initial concentration than on the initial height. The velocity of the particles are may be affected by the wall of the cylindrical vessel used.

Clear liquid interface height, z, cm

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CONCLUSIONS AND RECOMMENDATIONS

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Fig. 9. Clear Liquid Interface Height vs. Settling Time (same initial height, different concentrations)

As observed from the Fig. 9, evident differences in their plots are present. A linear behavior is observed at the start of sedimentation although the sample with the highest initial concentration flattened out the quickest.

settling velocity (cm/hr)

Settling velocity vs. Concentration

It can also be concluded that increasing the initial mixture concentration decreases the settling velocity of the particles before the compression settling zone. During the compression settling zone, the higher concentrations would result to higher settling velocities. It was also observed that the sedimentation process obeyed Stokes Law, and that the drag force FD, Reynolds number NRe, and terminal settling velocity vt behaved in a similar manner. REFERENCES

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Foust, A.S. (1980). Principles of Unit Operations. Singapore: John Wiley & Sons (Asia) Pte Ltd. pp. 629-636 Geankoplis, C.J. (1993). Transport Processes and Unit Operations. Singapore: Prentice Hall. pp. 816-817, 820, 825 McCabe, W.L. (2001). Unit Operations of Chemical Engineering. Singapore: McGraw-Hill Book Co. pp. 164, 168, 1039-1040 0.00

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http://www.mineralco.net/kaolin/index.php. Retrieved February 29, 2008

concentration (g/L) 5.50%

7.50%

2.50%

http://ceeserver.cee.cornell.edu/jjb2/cee656/Sediment-lect.doc. Retrieved February 29, 2008

Fig. 10. Settling Velocity vs. Concentration (same concentration, different height)

Settling Velocity vs Settling Time (Varying Initial Concentrations) 200

Settling Velocity, vt, cm/hr

Based on all the data and graphs gathered from this experiment, it can be concluded that the initial concentration and height (or volume) of the slurry affects its sedimentation characteristics. In particular, increasing the initial height of the slurry would also increase the settling time needed to reach the final height and somewhat increase the settling velocity.

7.50%

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5.00% 2.50% 100

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0 Settling Time

Fig. 11. Settling Velocity vs. Settling Time (same initial height, different concentrations)

In accordance with theory, the more concentrated sample had lower settling velocity, as shown in Fig. 11. Greater number of solids block the water below from rising up, thus the solids take longer to settle down. However, as the particles reach the compression settling zone, the trend is reversed, that is, the more concentrated sample had faster settling velocity. This is probably because the weight of the solids that compress the particle matrix is the determining factor in the compression