Analysis of the Effect of Slurry Concentration and Height on Sedimentation Chara cteristics 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 predi ct that initial slurry concentration and height affect the sedimentation charact eristics, particularly settling time and settling velocity. From experimental da ta, it was shown that the settling velocity of a mixture decreases with increasi ng concentration, yet reverses trend in the compression settling zone; and settl ing time needed to reach the final height increases with increasing initial slur ry height. Keywords: compression settling, critical settling point, drag force, free settling, hindered settling, rate-limiting layer Stokes Law, terminal veloc ity OBJECTIVES The experiment aimed to observe the relationship of settling time with slurry concentration, as well as with initial slurry height. This experime nt also intended to determine the behavior of settling velocity as the sedimenta tion process proceeds. The effect of slurry concentration with particle settling velocity was also studied. THEORETICAL BACKGROUND Sedimentation is one of the m ethods used in industry to separate liquid-liquid or solid-liquid mixtures. By d efinition, sedimentation is the separation of a dilute slurry or suspension by g ravity settling into a clear fluid and a slurry of higher solids content (Geanko plis, 1993). The resulting liquid is essentially particle free. In industry, eit her the particle free liquid or the particles itself is the desired product. Bas ically, sedimentation is the movement of particles through a fluid. All througho ut its motion, three forces act on the particle, namely, buoyant force, gravitat ional 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 Equati on 2 gives the terminal velocity for free settling wherein a particle is at a su fficient 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 sett ling because of the interference of the other particles, thus the settling veloc ity for hindered settling is less than that for free settling. (Geankoplis, 1993 ) The terminal velocity becomes a function of e, th volum fraction of th slurry
mixtur occupi d by th liquid. S v ral corr lations hav b n d v lop d to ana lyz s ttling v locity for hind r d s ttling, and th ir m thods and d rivations ar b yond th scop of this xp rim nt. PROCEDURE Th xp rim nt involv s th a nalysis of th ff ct of varying th h ight of th slurry and th ir conc ntratio ns on th s dim ntation prop rti s. To d t rmin th ff ct of initial slurry h ight on s dim ntation prop rti s, thr sampl s with th sam conc ntration of 2 .5% kaolin-wat r solution w r mad . Initial slurry of 800 mm, 600 mm and 400 mm w r assign d. Th slurry insid th v ss l was nsur d to hav a homog nous ch aract ristic by rigorously mixing and shaking th s dim ntation cylind rs. Start ing at th sam , th mixtur s w r allow d to s ttl , and at int rvals of 2 minu t s, th h ights of th cl ar r gions of th thr sampl s w r r cord d. Total obs rvation tim was 2 hours. For th s cond part of th xp rim nt, th ff ct of conc ntration on th s dim ntation prop rti s was analyz d. Th volum (or h ight) of thr n w sampl s was mad constant, and th ir conc ntrations ar vari d (2.5%, 5%, 7.5%). Th h ights of th cl ar r gions w r r cord d with int rval s of 2 minut s for th first two hours. Th sampl s w r l ft ov rnight and th last point was to b r cord d at that p riod. For this xp rim nt's cas , mor tha n tw nty-four hours was obs rv d. wh r m/rp is the volume of the pa ticle, r is the density of the liquid, and g is t he g avitational constant. The g avitational fo ce, Fg, on the pa ticle is given by Newton's Law as The d ag fo ce, FD, is the f ictional esistance elated to th e velocity head of the fluid displaced by the moving body (Geankoplis, 1993) and is given by the equation
whe e CD is the dimensionless d ag coefficient, and is velocity head. The d ag c oefficient is a function of the Reynolds numbe . In the lamina flow egion whe e NRe<1, Stokes' Law dominates and CD is given by (Geankoplis, 1993) (1) In sedime ntation, the pa ticles expe ience a pe iod of accele ated fall and a pe iod of c onstant velocity fall (Geankoplis, 1993). The constant velocity pe iod is usuall y of mo e impo tance, as the accele ated fall pe iod is ve y sho t elative to t he constant velocity pe iod. In the constant ate pe iod, the pa ticles each a maximum settling velocity known as the te minal velocity, vt. The te minal veloc ity is dete mined by solving the velocity at which the sum of the th ee fo ces i s equal to ze o. Geankoplis gives the equation fo the te minal velocity of sphe es as (2) whe e Dp is the pa ticle diamete .
RESULT AND ANALYSIS The mechanism of solid settling f om slu ved in a glass cylinde as shown in Fig. 1 below. 90 80 70 60 50 40 30 20 10 0 0.00
y can be best obse
Clea Liquid Inte face vs. Settling Time (Va ying Initial Heights) Clea liquid inte face height, z, cm tube 1 tube 2 tube 3 0.50 1.00 Settling time, q, hr
1.50 2.00 Fig. 2. Clear Li uid Interface vs. Settling Time (same concentration, different initial heights) Fig.1 . Batch Sedimentation (Source: McCabe, 2001) Initially, the slurry is unif ormly concentrated and the initial height is zo, as shown in Fig. 1a. The concen tration of the slurry is high enough that the particles affect each other's rate o f fall to the extent that after a short time, all particles settle at the same v elocity and are assumed to approach rapidly the terminal velocities under hinder ed-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 faste r, thus forming zone D shown in Fig. 1b. Zone A is the region of clear li uid (F oust, 1980). Zone B is a region of uniform concentration which is essentially e ual to the initial slurry concentration (McCabe, 2001). In this zone, the partic les 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 t he particles are varied (Foust, 1980). As sedimentation goes on, the depth of zo ne B decreases, the depths of zone A and D increase, while that of zone C remain s constant, as shown in Fig. 1c (McCabe, 2001). Zone B eventually disappears, an d the solids in zone C and D merge such that only zone D is distinct, as shown i n 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 co mpression 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 criti cal settling point. By definition, it is the point at which a single distinct in terface forms between the clear li uid and sediment (Foust, 1980). Beyond the cr itical settling point, sedimentation occurs by compression. The gradual accumula tion of the upper particles compress the solids at the bottom and decrease the h eight of zone D, and force the residual li uid in zone D out upward through the solids into the clear li uid zone. The settling rates during compression settlin g are very slow, and the rates may be estimated using hindered settling computat ion 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 concentrati on 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). One of the objectives of this experiment is to determine the effect of varying initi al slurry heights (or volume) on the sedimentation characteristics. Initially, t he concentrations of the three samples were kept constant and their initial heig ht 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 de
pth 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 sedim entation goes along, as shown by the steep linear part of the plot. The plot als o 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 s till almost linear. The part of the plot that is almost horizontal represents th e compression settling stage, wherein hindered settling dominates. Fig. 3. Getting the zone settling velocity (Source: www.ceeserver.cee.cornell.ed u) As shown by Fig. 3, the settling velocity for the different regions can be deter mined from the plot of li uid interface height versus time. The slope of the ste ady interface subsidence rate represents zone settling velocity. Tube 1: Determination of Velocity 900 800 Clear li uid interface height 700 600 500 400 300 200 100 0 -20 0 20 40 60 Settling time 80 100 120 140 Fig. 4. Determining the settling velocity
Fig. 4 shows the method used in this experiment to determine the settling veloci ties at different points. The slopes of the tangent lines at each point, which i s e ual to the settling velocity at the point, were determined. In e uation, (3) The exact values of the settling velocities of each trial are shown in the appe ndix. From the y-intercept of the tangent lines in Fig. 4, the height zi that th e 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, u sing the e uation (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 the nearer presence of the other particles slow each other's settling velocity. Th e velocity in the compression settling zone is significantly less than that in t he earlier region. Fig. 5 also shows how the initial height (or volume) of the m ixture affects the settling velocity of the mixture. The sample with the highest initial height (namely, tube 1) had, in general, the fastest settling rates com pared to rates of the other samples. Tube 1: Height vs. Time 900 Clear li uid interace height, z, cm 800 700 600 500 400 300 200 100 0 0 20 40 60 Settling time, q, hrs 80 100 120 200 180 Settling Velocity (cm/hr) 160 140 120 100 80 60 40 20 0 0.00 50.00 100.00 150.00 200.00 250.00 Fig. 7. Getting the critical settling point Concentartion (g/L) tube 2 tube 3 tube 1 Fig. 5. Settling Velocity vs. Concentration (same height, different concentratio n) Time, mins As the sedimentation process goes along, the concentration of increasingly becomes more concentrated because the solids are cted. As this happens, the settling velocity decreases as the eases, as shown in Fig. 5. Notice that the velocity decreases nt rate when the concentration is relatively low. Settling Velocity vs. Settling Time 200 180 160 140
the solids region getting more compa concentration incr at almost a consta
Additional information that can be determined from the z vs. q plot is the critica l settling point, as illustrated in Fig. 7. The critical point is the point wher e a single distinct interface forms between the clear li uid 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 h and, 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 ex tended until they intersect. The angle between these two lines is measured and a n angle bisector is used. The bisector is extended until it touches the curve. T he point of intersection is the critical point. A tangent line is made at the cr itical 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 31 26 21 16 0 200 400 600 800 1000 Initial Height, mm tube 1 tube 2 tube 3 Settling velocity, vt, cm/hr 120 100 80 60 40 20 0 0.00 0.50 1.00 Settling Time, q, hr 1.50 2.00 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 do esn't necessarily affect the sedimentation rate. For the second part of the experi ment, the objective was to determine the effect of initial concentration on sedi mentation characteristics. Three samples of kaolin-water slurry were made with d ifferent concentration. It is expected that the rate of descent of the solid-li uid interface is a function of local concentration (Foust, 1980). Fig. 6. Settling Velocity vs. Settling Time (same concentration, different initi al heights) Fig. 6 shows the trend of settling velocity as sedimentation goes along. It shou ld be noted that there are regions wherein the velocity is approximately constan t. The settling velocity also experiences significant change. It can be seen tha t the velocity decreases as the sedimentation goes along, as is theoretically ex pected. This is because the hindered settling region is increasingly becoming mo re concentrated as time goes on and
Height vs. Settling Time (Varying Initial Concentrations) 100 90 settling zone. The settling velocity used in Fig. 11 was computed using the meth od illustrated in Fig. 4. It should be noted from Fig. 6 and Fig. 11 that the zo ne settling velocity depends more on the initial concentration than on the initi al height. The velocity of the particles are may be affected by the wall of the cylindrical vessel used. Clear li uid interface height, z, cm 7.50% 80 70 60 50 40 30 20 10 0 0 10 20 30 40 Settling time, q, hours 50 60 70 5.0 0% 2.50% CONCLUSIONS AND RECOMMENDATIONS Based on all the data and graphs gathered from t his experiment, it can be concluded that the initial concentration and height (o r volume) of the slurry affects its sedimentation characteristics. In particular , increasing the initial height of the slurry would also increase the settling t ime needed to reach the final height and somewhat increase the settling velocity . It can also be concluded that increasing the initial mixture concentration dec reases the settling velocity of the particles before the compression settling zo ne. During the compression settling zone, the higher concentrations would result to higher settling velocities. It was also observed that the sedimentation proc ess obeyed Stokes Law, and that the drag force FD, Reynolds number NRe, and term inal settling velocity vt behaved in a similar manner. REFERENCES Foust, A.S. (1 980). 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 Operat ions of Chemical Engineering. Singapore: McGraw-Hill Book Co. pp. 164, 168, 1039 -1040 0.00 100.00 200.00 300.00 concentration (g/L) 5.50% 7.50% 2.50% Fig. 9. Clear Li uid Interface Height vs. Settling Time (same initial height, di fferent concentrations) As observed from the Fig. 9, evident differences in their plots are present. A l inear behavior is observed at the start of sedimentation although the sample wit h the highest initial concentration flattened out the uickest. Settling velocity vs. Concentration 180 160 140 120 100 80 60 40 20 0 settling velocity (cm/hr) http://www.mineralco.net/kaolin/index.php. Retrieved February 29, 2008 http://ce eserver.cee.cornell.edu/jjb2/cee656/Sediment-lect.doc. Retrieved February 29, 20 08 Fig. 10. Settling Velocity vs. Concentration (same concentration, different height) Settling Velocity vs Settling Time (Varying Initial Concentrations) 200 Settling Velocity, vt, cm/hr 150 7.50% 5.00% 2.50%
100 50 0 Settling Time Fig. 11. Settling Velocity vs. Settling Time (same initial height, different con centrations) In accordance with theory, the more concentrated sample had lower settling veloc ity, as shown in Fig. 11. Greater number of solids block the water below from ri sing up, thus the solids take longer to settle down. However, as the particles r each the compression settling zone, the trend is reversed, that is, the more con centrated sample had faster settling velocity. This is probably because the weig ht of the solids that compress the particle matrix is the determining factor in the compression
