Ind. Eng. Chem. Process Des. Dev. 1981, 20, 154-160
154
Theoretical and Experimental Studies of a Gravity Separation Vessel Jacob H. Masllyah' and Ted K. Kwong Department of Chemical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 206
Frederick A. Seyer Syncrude Canada Research, Edmonton, Alberta, Canada T6C 4G3
The performance of a pilot size gravity separation vessel has been investigated both experimentally and theoretically. The effects of the feed flow rate, the feed sand concentration, and the feed particle size distribution on the vessel performance were studied. A theoretical model simulating the gravity separation vessel was developed and it was in excellent agreement with the experimental findings.
Introduction In the past, there has been a strong emphasis on experimental and theoretical work on continuous and batch thickeners [Kynch (1952), Eklund and Jernqvist (1975) and Fitch (1975)l. However, little attention has been devoted to gravity separation vessels. Such vessels differ from continuous or batch thickeners in that they have a side stream and they operate below the critical flux. Typically, the feed stream contains solids having a wide range of densities and particle sizes. The gravity separation vessel is usually used to achieve a certain degree of separation between the various solids, and to a certain extent a gravity separation vessel is a type of a classifier. It can be considered to be related to the class of hydraulic classifiers [Taggart (1950) and Wills (1979)]. A generalized model applicable to tank or pool classifier has been successfully developed by Fitch (1973) based on differential settling, albeit such a model is for very dilute slurries. Such a model could be extended to include hydraulic classifiers and gravity separation vessels. This study has been prompted by the use of gravity separation vessels in the Clark hot water method (1930) for processing Athabasca oil sands. In Clark's process the oil sand is first treated with steam and caustic soda in a conditioning drum. The oil sand slurry is then fed to a gravity separation vessel where the bitumen in the form of a dispersion floats to the top of the vessel and forms a froth. This froth is then pumped into upgrading units for further processing. The sand particles leave the bottom of the vessel and are consequently fed into tailings ponds. Any bitumen carried out by the tailings stream is considered as a loss. A side stream carrying clay fines, sand, and bitumen, referred to as the middlings stream, is usually drawn from the middle of the vessel for further processing. It is evident that a good understanding of the operating characteristics of the gravity separation vessel as influenced by the slurry feed stream and operating conditions is essential for maximum bitumen recovery. Due to the complexity of the separation process of bitumen-sand/claywater as is encountered in the hot water process, it was felt desirable to work with a much simpler system where the physical properties are better defined and controlled. In part 1 of this work, separation of water-sand slurries was studied. In part 2 of this study, to be reported at a later date, polyethylene resin particles which are lighter than water are introduced to the sand-water slurry and the separation of polyethylene-sand-water slurry will be studied. 0196-4305/81/ 1120-0154$01.OO/O
The work reported here is only concerned with the study of the separation of sand slurries in a gravity separation vessel. The feed stream was introduced near the middle of the vessel. Two streams were withdrawn from the vessel, namely a middlings stream (a side stream) from the middle of the vessel and a tailings stream from the bottom of the vessel. The overflow stream rate is zero. Studies were made of the effect of the feed flow rate, the concentration of sand in the feed stream, and the sand particle size distribution on the sand recovery in the middlings and the tailings streams. A mathematical model describing the operation of the separation vessel was developed to gain a better understanding of the separation process. Description of the Equipment The pilot scale experimental extraction circuit is schematically represented in Figure 1. The closed flow system consisted of a 0.91 m X 0.91 m X 1.2 m feed preparation tank and a 0.91 m diameter stainless steel gravity separation vessel. Figures 2 and 3 show the geometry and the dimensions of the vessel. With no overflow, the vessel has two exit streams, the middlings and the tailings streams. The middlings stream was withdrawn from six equally spaced 2.5-cm diameter openings located circumferentially 0.3 m from the top of the vessel, whereas the tailings stream was pumped out from the bottom of the vessel. To facilitate the flow of sand in the lower section of the vessel, the lower portion of the separation vessel was designed to slope at angles of 45' and 63O, as is shown in Figure 2. Two vertical sections of sight glass were installed along the wall of the vessel and all the process streams had a section of clear plastic piping for flow observation. A level control system in which the middlings flow rate acted as the manipulated variable was utilized to control the slurry level in the vessel. A 3.8 cm i.d. feed pipe entered the separation vessel from the top and ita end was extended 12.7 cm below the top edge of the vessel. A plexiglass feed distributor having a diameter of 15.2 cm was held in place by a stainless steel bracket which was mounted on the feed pipe. The distance between the feed pipe tip and the distributor was set at about 9 cm. The sand slurry of the tailings and the middlings streams were recombined in feed tank and mixing was achieved using 3-hp and 'lChp agitators. In order to keep the amount of air entrained by the slurry in the feed tank to a minimum, a circular plate was placed along the shaft of the 3-hp mixer to prevent vortex formation. Two 0 1980 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 1, 1981 155
F-3
key: A- 1 F - I , 2, 3 M-1 P-1 P-2
P.3
-
=
3 h p Lightnin agitator Foxboro magnetic flow meters feed preparation tank 2L10H Moyno pump with 20 hp motor 2L10H Moyno pump with variable speed drive and 20 h p motor 1 L 6 Moyno pump with variable speed drive and 3 hp motor 1 L 6 Moyno pump with variable speed drive and 3 hp motor centrifugal pump with 3 h p motor (not used in present study) gravity separation vessel froth-collecting vessel (not used in present study) scraper unit (not used in present study) thermocouple locations of sampling ports
=
Cooling Coils
=
= = = =
P-4
=
P-5
=
s-1 s.2
= =
sc.1
=
T. 1 1,2,3
-
c
Figure 1. Schematic diagram of the flow system. 91.4 cm
I*
*I
I
t I
130.5 cm
t
130.5 cm
Middlings Withdrawalports
it
j 30.5 cm
1-1
30.4 cm
Figure 2. Side view of the gravity separation vessel.
-Middlings Withdrawals
Feed
1 Tailings Outlet
Figure 3. Top view of the gravity separation vessel.
Moyno pumps were available for supplying the feed to the separation unit. One of the pumps was situated directly
below the feed tank and its suction line was extended 0.6 m into the feed tank to avoid excessive sand settling into the pump during shutdown periods. The other Moyno pump, acting as a stand-by unit, also had a siphon suction line built for the same purpose. Butterfly valves were installed at the sudion side of both the Monyo pumps used for the middlings and the tailings streams. The flow rates of the feed, the middlings and the tailings streams were measured and recorded using Foxboro magnetic flow meters and Sandborn recorders. A thermocouple at the feed line provided a continuous monitoring of the feed temperature which was subsequently controlled by a cooling coil inside the feed tank. Three-way plug valves were chosen for collecting samples from the process streams for further analysis. The separation vessel was also equipped with an overflow pump and a froth scraper. However, as the overflow stream flow rate was always zero and no light particles were employed, IU) use was made of the overflow pump and the froth scraper in the present study. Experimental Procedure The sand used in this study was silica flour with a density of 2.65 g/cm3 and a particle size ranging from about 0.001 cm to 0.03 cm. The quartz-based silica flour supplied by Cardium Supply and Services was chosen rather than Ottawa Sand, because of its superior resistance characteristics to pump grinding. This is particularly important when a certain particle size distribution has to be maintained within the closed flow system for studying the individual effects of the flow parameters on the separation efficiency of the vessel. Experiments were conducted at a feed rate of either 1800 cm3/s or 2300 cm3/s and a feed sand volumetric concentration ranging from 0.18 to 0.25. Each feed rate or feed sand concentration was studied at a series of tailings flow rate which was run between 40 and 70% of that of the feed. All the experimental runs were started at room temperature. Steady state was assumed after an initial 2 h of continuous operation. Once samples from the feed, the middlings, and the tailings streams were taken, the tailings flow rate was changed and the sampling procedure was repeated at 1-h intervals. The collected samples were then analyzed for the sand composition. In selected runs, particle size distribution of the sand in each of the process streams was determined by sieving. Mathematical Modelling Traditional continuous and batch thickeners have been successfully analyzed using the concepts advanced by Coe and Clevenger (1916) and the theoretical work of Kynch (1952). The cornerstone of the analysis is based on the concept of critical flow; Le., the thickener output is governed by the rate at which the sludge at the bottom of the vessel transmits solids to the tailings stream. A gravity separation vessel operates below the critical flux and consequently the analysis applicable to traditional thickeners cannot be applied to gravity separation vessels. Moreover, in order to accommodate for the presence of the middlings stream and to be able to account for the effect of the feed solids particle size distribution, it is necessary to adopt a different approach in the modelling of a gravity separation vessel. The modelling approach is to utilize the continuity and the momentum equations for a multiparticle system as suggested by Wallis (1969) and to adopt these equations in the same manner as used for other flow situations [Shook and Masliyah (1974) and Masliyah (1979)l. The gravity separation vessel is assumed to be one dimensional and to consist of three zones, as is shown in
156
I1
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 1, 1981 Feed Stream Or
IJpper
2 0 1
The hydrodynamic interaction force between the fluid and the particles can be given by
Frofh Stream
,
fjk
= 3CDkPf (ufk - uJk)(ufk - uajkIat~/4dajF ( a f ~(Sa) )
*"SI.
\
Lower Zone
k=l,2
Middlings Stream 3 li
Middle Zone
with
/
k=l,2
and Tailings Stream
Resjk
a-
=
d6jPdU8jk
- ufklafM/pf
(54
Figure 4. Zone characterization of the mathematical simulation.
k=1,2
Figure 4. The middle zone is assumed to be well mixed whereby the solids concentration is uniform throughout the zone and no differential settling is considered [Fitch (1973)j. The solid concentration in the middlings stream is the same as the middle zone. The upper and the lower zones are considered to be solid-liquid transport beds and they do not enter in the analysis. In this model, it is assumed that the middle zone provides the solids (sand) to the upper and the lower zones of the vessel. Once a solid particle leaves the middle zone, it is then carried away by either the overflow or the tailings streams. The momentum equations are applied at the top and the bottom regions of the middle zone. The velocities of either the solids or the fluid at these regions are not necessarily the same. However, the solids concentration is the same throughout the middle zone. The mass conservation for the solids and the fluid is taken by considering the entire middle zone. The feed is assumed to be composed of N fractions each of which being characterized by a given particle diameter. The density of each fraction is the same. The governing equations defining the separation process in the gravity separation vessel are as follows. (a) Momentum Equations. Assuming rectilinear steady state flow, the momentum equation for the jth sand particle species is given by Wallis (1969)
The term F ( a f ~is) a function to account for the particle concentration in the middle zone. F(am) can be determined either from experimental correlations or through the development of a hindered settling model. The most ) due to Richaccepted forms of the function F ( a f M are ardson and Zaki (1954) and to B m e a and Mizrachi (1973): Richardson and Zaki correlation (1954)
0=
-(E) + k
k = 1, 2; j
+ fjk = 1, ..., N Psg
Subscript k = 1 and 2 refers to the upper and lower limits of the middle zone, respectively. The number of the particle species in the suspension is N. By neglecting wall effects and particle-particle forces, hydrodynamics equilibrium leads to N
+
j=l
"sjM f j k
=0
(3)
k=1,2 where am and a s l are ~ the fluid and the jth sand particle species volumetric concentration in the middle zone, respectively. The volumetric concentration for sand particle species and for the water yields N 1
aB]M
+ am = 1
F(am) =
[+ 1
(1 - afM)'/3 exP(
(4)
5(;---))]-1
(7)
The momentum equations for the j t h sand particle species and for the fluid equations (1) and (2), together with eq 3 to 5 can be solved simultaneously to give the velocity difference (slip velocity) between the various sand particles and the fluid
k = 1, 2; j = 1, ..., N where pM is the middle'zone suspension density and it is given by N
PM
k=l,2
(6)
= a%
and Barnea and Mizrachi correlation (1973)
(1)
The momentum equation for the fluid is given by
afM f f k
F(a,)
= Pf % +V PaICaajM
-
j=1
In the limit of Reajk 0, the above expression for the velocity difference becomes the same as that derived by Masliyah (1979). The slip velocity ( u ~ -h ufk) is governed by the difference between the solids and the suspension densities, the fluid viscosity, the particle diameter, and its Reynolds number. In order for the solids velocity at either the bottom or the top of the middle zone to be evaluated from eq 8, the fluid velocity and the middle zone suspension density must be known. To this end, the mass balance for the fluid and for the j t h sand particle will provide the necessary information to calculate ufk and p ~ . (b) Mass Conservation. The mass conservation for the j t h sand particle is given by (9) Q F ~ ~= ~QF~ a ~ j+ h lA(u8j2 - u8jl)asjM and the mass conservation for the fluid yields (10) Q F ~ W= Q M ~ N + A(un - u&m The terms A(unam) and A(uflam) represent the fluid flow rate in the tailings and in the overflow streams, respecand A(uEjlaEJM) represent the tively. The terms A(uEj2aEIM)
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 1, 1981 157
1
/I
Standard
+ Fine.
/
/
5
4 1
1 10
Standard Sand
20
40
Ji
Sand
I
4
I
i
I -I
4
QdQF
I
60 80 100
Figure 6. Sand recovery variation with feed split for the standard sand slurry. 200
r
400
Size of Sand Particles, pm (Diameter)
Figure 5. Particle size distribution of the various feed sand slurries.
mass rate of the jth sand particle size leaving in the tailings and in the overflow streams, respectively. It should be noted that the downward direction is positive and consequently, the upward fluid velocity un is a negative quantity. For a typical simulation of a gravity separation vessel, the feed flow rate and the feed sand concentration are specified as well as the feed sand particle size distribution. For a unique operation of the gravity separation vessel, two operating flow parameters are to be specified. In this study, the tailings density, p ~ and , the overflow rate, QP are specified. The tailings density is given by N
Ps PT =
1 N 1
usj2 %]M
+ Pfuf!? %U (11)
usj2 %]M
+ ut2
and the overflow rate is given by
Q,
(12)
= A~flam
+
Equations 8 to 12 and eq 4 provide 2N N + 1 + 1 + 1 + 1 (= 3N + 4) equations, respectively. The unknowns are CY,M, am, Vfk, usjk, and QM,leading to N 1+ 2 + 2N + 1 (= 3N + 4) unknowns, respectively. Due to the nature of the model an additional constraint was added, whereby no sand particle can enter the middle zone from the upper zone. Therefore for usjl > 0, the velocity usjl was set to zero. In this manner, sand can be carried out of the middle zone when lunl > luGll, but a sand particle cannot enter the middle zone as un 5 0 and uSI1 is always positive. The set of linear and nonlinear (3N + 4)equations defining the model together with the above mentioned constraint were solved by an iterative procedure utilizing under-relaxation Gauss-Seidel method and NewtonRaphson algorithm. Discussion of Results Experimental Studies. In this study, sand slurries having different sand particle size distribution (PSD)were used. The PSD are shown in Figure 5. The various PSD were obtained by mixing silica flour of different mean particle size. The sand has a specific gravity of 2.65. The sand slurry having the lowest amount of fines is referred to as “stand”, that with a higher fines content is referred to as “standard plus fines”, and that with the highest fines content as “standard plus extra fines”.
+
R W I 34.37 -& std sand Run # 3 8 . 4 1 Sld Flnes Run 86 - 68 Sfd + Elfla Fines
*
“0 3
+ +
05
+
07
:gF
I 0020 20 =
LOW
Q
LOWOF
0 2 2 Low 0;
1
O ’
09
Q P F
Figure 7. Sand recovery variation with feed split for the three types of sand slurries.
A summary of the experimental results are given in Table I. In all the experimental cases considered, the overflow stream Qp was set to zero flow. The error in the mass conservation measurements for the sand was within 5%. A close examination of Table I indicates that for given type of slurry, feed sand concentration, and feed rate, the middlings stream sand concentration is not a function of the tailings flow rate. In other words, for this system and for the range of variables studies, the operating conditions as manifested in the manipulated variable, QM or QT, does not affect the middlings stream sand concentration. i middlings Consequently,the percent sand recovered i ~the or in the tailings streams varies linearly with the feed split, QT/QF. The variation of the sand recovery for the standard slurry at two different feed flow rates is given in Figure 6. The percent sand recovered in the middlings stream is equal to 100QMaSM/QFa,F which is equal to 1 0 0 ( ( ~ , ~ / a ~ )QT/QF). (lWhen this quantity is plotted against QT/QF, a straight line will emerge only when (Y,M/LY,F is constant and independent of QT/QF. Table I indicates that (Y,M is independent of &(for given QF, as, and the type of slurry). Consequently, the linear relationship of QMa,M/QFasF with QT/QF is expected. The linear relationship between the percent sand recovered in tailings with QT/QF follows directly from the overall mass balance for the sand. The straight lines for the percent sand recovered in the middlings against the feed split, QT/QF, have a slope of -(aH/ag). Comparison between the lines for low and high feed flow rates (same values of as) indicates that the middle zone sand concentration becomes higher when the feed flow rate is increased.
158
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 1, 1981
i1 Standard Sand
13' 800
'
I
1000
'
1
1200
"
I400
'
1
I600
02
06
04
Flow Rate of Tailings, QT cm3/s
Figure 8. Variation of tailings density with tailings rate for different feed rates.
08
10
QT'Q,
Figure 10. Variation of tailings density with feed split for standard and standard plus fines sand slurries.
I
1 7 < 0
,
i i
16
\ 13-
02
QdQ,
Figure 9. Variation of tailings density with feed split for different feed sand concentrations.
101
'
03
04
I
,
,
,
05
06
07
08
,
09 QTIQF
IO
A similar plot is shown in Figure 7 for the different sand
Figure 11. Variation of normalized tailings density with normalized tailings flow rate.
feed slurries. The sand recovery in either the tailings or the middlings streams is much affected by the sand particle distribution of the feed stream. In other words, the sand concentration in the middle zone is a strong function of the feed slurry particle size distribution. For the high fines content feed slurry, the middling zone has the highest sand concentration. Consequently, for a given feed split, QT/QF, the sand recovery in the tailings stream is lowest for the high fines content slurry. The amount of fiies in the feed slurry obviously has much influence on the performance of the gravity separation vessel. In the operation of a gravity separation vessel, the tailings density is usually used as the controlled variable. Consequently, it is important to study the effects of the flow parameters, e.g., feed flow rate, on the tailings density. The effect of varying the feed slurry volumetric flow rate on the tailings density is shown in Figure 8 for the case of standard plus extra fines slurry. The feed sand concentration is 0.25. Figure 8 indicates that for the case of a higher feed rate, a higher tailings rate is needed to maintain the same tailings density. Similar behavior was observed for the other feed slurries. The effect of the trailings density due to different feed sand concentration for a constant feed rate is shown in Figure 9 for the case of standard plus fines slurry. The curve pT vs. QT/QF for the case of a higher feed sand concentration lies above that for the case of a lower concentration. To maintain the same tailings density, the tailings flow rate is higher for the case of a more concentrated feed slurry. The effect of the feed slurry particle size distribution on the tailings density is shown in Figure 10 for the case of standard and standard plus fines slurries. The feed rate
is about 2300 cm3/s and the feed sand concentration is approximately 0.20. For a given feed split, the tailings density is a strong function of the fines content of the feed slurry. To maintain the same tailings density, the tailings rate is lower for the case of the feed slurry containing more fines. From Figures 8 to 10, it is evident that the tailings density is much affected by the feed flow rate, the feed sand concentration, and the feed slurry particle size distribution. The effect of the first two variables can be minimized by plotting a tailings density ratio p T / w against the feed split, QT/QF as is shown in Figure 11. For a given sand slurry type a plot of p T / p ~vs. QT/QF could be used for design purposes for a situation not very dissimilar from the experimental conditions of this study. Simulation Studies. The solution of the set of equations presented by the hindered settling relationship (8), and the conservation equations (9) to (12) for a given set of input data provided the tailings and the middlings streams flow rates and the sand particle distribution in the exit streams. It was found that Barnea and Mizrachi hindered settling relationship provides a better agreement with the experimental results than that of Richardson and Zaki correlation. The latter relationship gives a lower drag for a given sand concentration. This is to be expected as Richardson and Zaki relationship does not hold well at low concentrations, e.g., below 0.07. Figure 12 shows a comparison of the mathematical model with the experimental results for the standard sand slurry. The agreement between the model prediction of the tailings density and the experimental values is fairly
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 1, 1981
150
Table I. Summary of Experimental Results rates, cm3/s run no.
feed
middlings
26 27 28 29 30 31 32 33 34 35 36 37
2253 2210 2235 2236 1673 1701 1698 1681 1678 1681 1687 1661
1243 1072 833 555 990 852 662 442 927 839 67 5 4 23
38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53
1733 1768 1739 1654 1737 1779 1753 1689 2305 2304 2293 2308 2314 2299 2306 2309
1091 927 726 442 1104 915 694 473 1230 1148 883 631 1577 1230 1041 713
54 55 56 57 58 59 60 61 62 63 64 65 66 67 68
1819 1818 1833 1839 2300 2313 2338 2313 2305 2282 2361 2364 1780 1793 1786
1028 852 662 50 5 1356 1156 978 705 1400 1117 883 757 1041 84 5 599
sand concn, vol. fraction tailings feed Standard Sand 1028 1161 1419 1684 694 845 1035 1262 7 57 852 1028 1262
middlings
tailings
density, g/cm3, tailings
0.0342 0.0340 0.0354 0.0371 0.0200 0.0172 0.0191 0.0254 0.0237 0.0257 0.0233 0.0272
0.422 0.370 0.313 0.262 0.428 0.357 0.303 0.259 0.442 0.405 0.348 0.290
1.696 1.611 1.517 1.432 1.707 1.589 1.499 1.428 1.729 1.668 1.575 1.479
0.0485 0.0494 0.0482 0.0445 0.0454 0.0477 0.0454 0.0450 0.0530 0.0538 0.0530 0.0535 0.0584 0.0592 0.0602 0.0581
0.475 0.383 0.324 0.283 0.415 0.330 0.285 0.251 0.340 0.320 0.271 0.238 0.462 0.356 0.306 0.263
1.783 1.632 1.535 1.467 1.684 1.544 1.470 1.414 1.561 1.528 1.448 1.394 1.763 1.588 1.504 1.434
0.114 0.115 0.114 0.114 0.124 0.125 0.125 0.122 0.111 0.114 0.114 0.114 0.099 0.099 0.099
0.420 0.368 0.323 0.299 0.420 0.372 0.332 0.307 0.411 0.337 0.300 0.288 0.387 0.321 0.285
1.693 1.606 1.532 1.494 1.693 1.614 1.548 1.507 1.679 1.556 1.495 1.476 1.639 1.530 1.471
0.201 0.197 0.202 0.205 0.181 0.189 0.192 0.184 0.207 0.210 0.210 0.208
Standard Sand Plus Fines 656 852 1022 1230 631 871 1072 1230 1072 1155 1419 1684 7 26 1072 1262 1590
0.199 0.202 0.204 0.207 0.181 0.181 0.182 0.184 0.188 0.189 0.183 0.185 0.191 0.196 0.197 0.203
Standard Sand Plus Extra Fines
1 8 1 ,
,
,
,
,
,
7 89 965 1167 1325 946 1161 1356 1609 915 1163 1482 1609 738 9 34 1186
,
,
0.249 0.250 0.250 0.255 0.244 0.248 0.247 0.251 0.224 0.229 0.228 0.232 0.219 0.225 0.224
, I60
700
PO0
1100
1300
1500
F
1700
Flow Rate of Tailings, QTcm3/s
Figure 12. Comparison with the simulation model for the standard sand slurry.
good. Similar close agreement was found for the other feed slurries. A more severe test of the mathematical model is in its capability to predict the particle size distribution in the tailings and in the middlings streams. The particle size distribution predicted by the model of the three types of sand slurries is in good agreement with the experimental results. The case for the standard plus extra fines slurry is shown in Figure 13. This close agreement indicates that
Standard Run x 58
c
*t 11
IO
T
Extra Fine. Sand
-
Experimental
----Model
I
20
, 40, , 60 I
, I l l
80 100
I
200
,
400
Size of Sand Particles, pm (Diameter)
Figure 13. Prediction of PSD for the standard plus extra fines sand slurry.
160
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 1, 1981
is in good agreement with the experimental results. Acknowledgment The authors wish to thank Syncrude Canada Research for its permission to publish the present work. a01
IS0
'
'
2100
'
' 2500
'
'
2900
'
3300
'700
Flow Rate of Feed OF c r n 3 / s
Figure 14. Sand recovery variation with feed rate for the three types of sand slurries.
the present model does not only predict accurately average quantities, but individual particle size concentration as well. It is interesting to note that the present mathematical model does not consider the relative positions of the feed distributor nor of the middlings withdraw ports. Moreover, it does not take into consideration the flow pattern in the vessel. The assumption of a well-mixed middle zone appears to described adequately the present gravity separation vessel operating with a sand-water slurry. As a final note, simulation of the effect of increasing the feed rate on the sand recovery in the tailings stream at a given feed split, QT/QF, is shown in Figure 14. From an operational point of view, keeping the same feed split for a given type of a feed slurry and increasing the feed rate results in little change in the sand recovery in the tailings stream. This type of behavior illustrates the flixibility of the gravity separation vessel while dealing with one type of a feed slurry. However, Figure 14 indicates that the particle size distribution of the feed slurry has a marked influence on the operation of the gravity separation vessel. For example, operating with the same feed split, QT/QF, of 0.4,in order to achieve a sand recovery in the tailings of 8590, the feed flow rates for the standard, the standard plus fines, and the standard plus extra fines slurries become 3000, 2000, and 300 cm3/s, respectively. Consequently, any design of a gravity separation vessel should take into account the feed particle size distribution. Conclusions In conclusion, the characteristics of the gravity separation vessel can be summarized as follows. (1) The middlings stream concentration is independent of the tailings stream flow rate. (2) The tailings density is a strong function of the feed flow rate and the feed sand concentration for a given tailings flow rate. (3) The sand recovery and the middle zone sand concentration are very strong functions of the feed particle size distribution. (4) For a given feed slurry, a plot of tailings to feed density ratio with tailings to feed flow rate ratio tends to minimize the effect of the feed flow rate and the feed sand concentration. Such a plot can be used for design purposes. (5) The developed mathematical simulation of the separation vessel
Nomenclature A = separation vessel cross-sectional area CD = drag coefficient d = diameter of the jth sand particle size $/dx = pressure gradient ff = drag force exerted by the particles on the fluid per unit volume of fluid f j = drag force exerted by the fluid on the jth sand particle size per unit volume of the jth sand particle size F = a hindered settling function, dimensionless g = gravitational acceleration N = total number of sand particle species Q = volumetric flow rate v f = fluid velocity relative to a stationery observer us, = jth sand particle size velocity relative to a stationery observer Greek Symbols af= volumetric concentration of the fluid a, = volumetric concentration of the sand asj = volumetric concentration of the jth sand particle size
= fluid viscosity pf = density of fluid pM = suspension density in
the middle zone sand density Subscripts f = fluid F = feed stream k = 1, interface between middle zone and upper zone k = 2, interface between middle zone and lower zone M = middlings stream or middle zone T = tailings stream p, =
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Received for review January I , 1980 Accepted August 20, 1980
