Ind. Eng. Chem. Res. 1997, 36, 5015-5022
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Continuous Sampling of Floating Solids Suspension from a Mixing Tank Nenad Kuzmanic´ * and Edita M. Kessler Faculty of Technology, Laboratory of Chemical Engineering, University of Split, Teslina 10/V, 21000 Split, Croatia
The problem of continuous wall sampling of monomodal suspension of floating solids from a stirred vessel at complete suspension state has been studied. Dispersion and sampling of floating particles was carried out in a vessel with impeller/baffle configuration usually recommended for suspension of solid settling particles. The dependence of the sampling efficiency on the characteristics of suspension (bulk solids concentration and particle size), sample tube design, and sampling technique (withdrawal velocity, mixer speed, and location of sampling) were investigated in detail. The results are, to a considerable extent, related to solid particles low inertia, pronounced effect of the upward buoyant force, and the complex hydrodynamics in the mixing vessel. At complete suspension state it is practically impossible to obtain a representative sample of floating suspended solids in a slurry tank with axial flow by sample withdrawal. Sampling errors can be minimized changing the suspension conditions and sampling technique, pointing to a great caution when this method is applied in practice. Introduction
FrJS ) k(D/T)p(∆F/FL)q
Several chemical engineering operations of considerable industrial importance, such as dissolution, leaching, crystallization, and liquid/solid reaction, involve the suspension of solid particles in a liquid phase in adequate mixing equipment. The solid particles usually need to be suspended completely in order to attain the maximum interfacial area between the solids and liquid phase and to avoid the accumulation of solids at any position of the apparatus (Conti and Gianetto, 1986). In fact, the aim of this procedure is to obtain a uniform suspension of solid particles in the liquid and to intensify the reduction of diffusion resistance in the system (Nagata, 1975). Most industrial solid/liquid mixing systems involve the suspension of solid particles heavier than the liquid. However, there are several applications where solids are lighter than the liquid and require a drawdown action to produce homogeneous slurries. The suspension of floating solids in liquids by agitation is of particular interest in the fields of fermentation, mineral processing, sewage treatment, and polymerization reactions (Hemrajani et al., 1988). Compared to the wide range of use and importance of the operation, surprisingly few papers can be found in the literature. The majority of papers published are based on the results related to the influence of vessel geometry, solids mass fraction, and impeller type on the just-suspended stirrer speed and associated power consumption (Ellis et al., 1988; Thring and Edwards, 1990; Armenante et al., 1991). In one of the pioneer papers in this field Joosten et al. (1977) recommended for this type of suspension a mixing vessel with a single partial baffle 0.2 T wide, immersed at the top of the liquid to a wetted depth of 0.3 T, axial impeller of 0.6 T and the impeller height above tank bottom of 1/9-3/9 T as the optimum configuration. They correlated the minimum drawdown speed for their preferred configuration, in which case an eccentric vortex draws the solids down, by * Author to whom correspondence should be addressed. Fax: +385-21-34 16 24. Telephone: +385-21-34 16 33. Email:
[email protected]. S0888-5885(97)00201-7 CCC: $14.00
(1)
Published papers suggest that the complete drawdown of floating solids by agitated liquids in stirred tanks can be achieved by two different mechanisms. It was found that, in the baffled tanks, in which the formation of the vortex was suppressed by the presence of the baffles, the intensity of turbulence is primarily responsible for particle dispersion. In this case energy dissipation and position of the impeller with respect to the liquid surface were found to be the controlling parameters. When alternative baffle configurations were used instead, it was found that the liquid swirl in tanks provides a mechanism for pulling down the floating particles into the bulk. This was observed to be a two-step process. In the first step, the centrifugal forces resulting from the swirl moved the light particles along the liquid surface from the walls of the tank into the “cone” of the vortex. There the liquid velocities were high enough to incorporate the particles into the bulk liquid being circulated by the agitator. The second step of high-velocity particle transport in the vortex was observed to be the controlling step (Armenante et al., 1991; Hemrajani et al., 1988). Information on local solids concentration, composition, and size distribution is often of great importance in order to control and operate with the equipment for handling slurry. A number of methods have been used to measure solids concentration, but wall sampling, for its simplicity and versatility, is widely adopted in the industrial practice. This technique uses small apertures in the wall of the equipment and different sampling devices that tend to disturb the fluid flow in the system the least possible. However, a representative sample that is identical in all properties to the system being sampled at the point of sampling is extremely difficult to obtain. Sampling errors arise mainly as a result of particle inertia relative to that of an equal volume of fluid. As a result of this inertia, fluid and particle velocity vectors at the sampler inlet will no longer be collinear. Thus, the errors depend on two main factors: the extent to which the sampling process disturbs the flow and how the particles respond to this disturbance. © 1997 American Chemical Society
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The effectiveness of sampling devices is usually expressed as the ratio of the measured solids concentration of the withdrawn sample and the local solids concentration in the slurry system at the point of sampling (C/C0). In literature this ratio is known as the separation coefficient, aspiration coefficient, or sampling efficiency (Nasr-El-Din, 1989). Up to now isokinetic and nonisokinetic wall sampling from slurry pipelines have been deeply investigated both theoretically and experimentally (Nasr-El-Din et al., 1985a,b, 1989, 1991). Much less investigation has been carried out on sampling from stirred tanks. The relatively low activity on this topic is probably due to difficulties connected with complex hydrodynamic phenomena in mixing vessels. In any case, continuous sampling from a stirred tank is much more complex than that from slurry pipelines, for two main reasons: (a) there are large differences in solids concentration along the vertical axis of the vessel, due to competing effects of turbulent dispersion and (b) the map of the fluid velocity in the stirred vessel (modulus and direction) is generally not sufficiently known, and in no case simple. The papers by Rushton (1965), Rehakova and Novosad (1971), and Sharma and Das (1980) belong among the rather important ones in this field. They investigated the effect of the withdrawal flow velocity on the sample solids concentration, using a straight probe in the plane of the Rushton turbine and developing empirical equations for a separation coefficient. Janse (1977) measured the separation coefficient in a crystallizer using a L-probe at the wall and investigated the influence of withdrawal velocity, and particle size and length of probe insertion. Significant variations were observed, depending on the particle inertia parameter. Recently, Kuzmanic´ et al. (1992), Barresi et al. (1993, 1994), and MacTaggart et al. (1993) did some basic work on sampling of suspension, pointing to the large effects of the sample tube design, withdrawal velocity, and sampling device location in the vessel on the sampling efficiency. However, the objective of all cited works is related only to the wall sampling of the suspension of settling solids from the mixing tank. The problems of sampling of floating solids from a stirred tank have not yet been systematically studied. Therefore one of our principal aims of this work is to investigate the possibility of obtaining a representative measure of the local floating solids concentration in a slurry mixing tank by sample withdrawal. At the same time, the paper aims to analyze the influence of the sampling technique, sample tube design, and characteristics of monomodal suspensions of floating solids on sampling efficiency, under isokinetic and nonisokinetic conditions, at complete suspension state. Experimental Setup and Procedure Measurements were taken in the mixing apparatus similar to that employed in previous investigations by Barresi et al. (1987) and Kuzmanic´ et al. (1992) which is schematically drawn in Figure 1. A flat-bottomed plexiglas stirring vessel (T ) 0.322 m) with four baffles of standard size (B ) T/10) at 90° was employed. The suspension was stirred by a 45° pitched four-blade turbine, pumping downward (D ) T/3). The impeller speed was controlled by an electromotor of a variable speed and a digital controller. For safety, the agitation
Figure 1. Schematic drawing of the experimental setup. 1. Vessel. 2. Stirrer. 3. Pump. 4. Solenoid valve. 5. Timer. 6. Variable-speed motor. 7. Optical tachometer. 8. Sieve and measuring cylinder. 9. Sampling probe. Table 1. Physical Properties of the Floating Solidsa NJS (rev‚min-1) at C h (kg‚m-3) d × 106 (m)
Fp (kg‚m-3)
5
7.5
10
120/150 300/400 400/500
840 835 835
728 725 732
730 725 728
730 725 735
a
Polyethylene (LDPE).
speed was from time to time checked with a stroboscope. The stirrer clearance was always equal to H/3. In each experiment the agitation speed was increased until complete drawdown was achieved. Complete drawdown was defined according to the Joosten visual criterion of stagnant zones (Joosten et al., 1977). In this case, the just-suspended stirrer speed NJS was defined as the speed at which stagnant zones at the liquid surface had just disappeared. Minimum stirrer speeds required for the just-suspended state are given in Table 1. A series of 20 runs showed that maximum positive and negative deviations from the mean NJS were about 2%. For determination of this state Bakker and Frijlink (1989) recommend a method similar to Zweitering criterion; that is these authors believe that the fully suspended state is obtained when no particle remains on the surface of the continuous phase for more than a second. Preliminary measurements showed that these two methods gave the same results. Eight equally spaced sampling tubes were vertically positioned along the vertical axis, in the middle plane between adjacent baffles. Three different sampling probes were tested: a simple straight sampling probe, a tube with a 45° cut edge, and an L-shaped probe (Figure 2). All the probes had 8 mm i.d. and a relative wall thickness δt (wall thickness/probe inside diameter) of 0.125. The openings of the probes were placed at 32 mm from the tank wall. These dimensions were kept constant and varied only when they had to meet the requirements of the nature of experiments. Slurry was withdrawn from the mixing vessel at defined points, continuously circulated in the shown system, and returned to the vessel at a point diametrically opposite the point at which it was removed.
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Figure 2. Sampling devices: a. Blunt tip probe. b. 45°-angle probe. c. L-shaped probe.
) 600 rev‚min-1. The linear correlation between the local fluid velocity and stirrer speed has been established and verified at several points in the tank which allows an easy recalculation of local fluid velocities for other values of the stirrer speed. Good agreement was observed between the values measured and those reported in literature, determined by other methods in geometrically similar systems (Jaworski et al., 1991; Geisler and Mersmann, 1988). Preliminary studies showed that the sample solids concentration changed with the sampling time. The sampling time was experimentally determined using different size solids, different solids concentrations, different sampling probes, and different axial sampling positions. The time of 10 s was generally adopted as optimum since the sample solids concentration does not change after longer periods of time. Reproducibility of the measurement was also established to be best at this sampling time. Samples were withdrawn 6 min after starting the mixer since this was a reasonable period for the system to reach the steady state. Results and Discussion
Figure 3. Map of the average velocity in the vessel.
The suspension was continuously removed using a variable speed impeller pump. Samples were taken by the flow being diverted into the collecting device by means of a solenoid valve controlled by a timer that allowed adaptation and control of the sampling time. The sample mass from a sieve, volume of liquid collected in a measuring cylinder, and sampling time were measured to determine the sample solids concentration and the sampling velocity. Monomodal suspensions of low-density polyethylene particles, the basic physical properties of which are shown in Table 1, were used as floating solids. Tap water (FL ) 1000 kg‚m-3) was used as a fluid in all experiments, and its height in the tank was equal to the tank diameter (H ) T). The knowledge of the fluid velocity in the vessel is necessary in order to evaluate the isokinetic sampling velocity. The local mean liquid velocity and the direction of the velocity vector in the vessel were measured using a modified Pitot five-hole tube similar to that realized by Barthole et al. (1982). Figure 3 presents a map of the average velocity in the used vessel, but it shows only the axial and radial components because the tangential component is generally nil or very small. The local average velocity pattern has been measured at N
Wall sampling of floating solids suspension from a mixing tank was undertaken to establish whether it is possible to obtain a representative sample, that is a sample identical in all properties to the system being sampled at the point of sampling. The study carried out is also of interest for the systems of continuous suspension withdrawal from stirred vessels. In the continuous processes the composition of the suspension in the withdrawal tube may be different from the average one in the apparatus; for proper design and operation it would be very useful to find the dependence of concentration and particle size distribution on the geometric characteristics of the sampling probe and on the sampling conditions (Baldi et al., 1981; Barresi et al., 1988). Experiments were conducted in a reactor system with the stirrer/baffle configuration usually recommended for settling solids suspension. Even though some authors for suspension of these kinds of particles recommend mixing tanks with partial baffles and an axial stirrer of nonstandard dimensions (D/T > 1/3), the above mentioned apparatus was used in this work for various reasons. Namely, in practice both settling and floating particles are frequently present simultaneously in a system so that both should be suspended. Therefore, this study would be taken just as preliminary in this respect. In addition, if a tank with partial baffles were used, a developed vortex would produce surface aeration. In this case the air incorporated into the liquid as well as the presence of the vortex may significantly disturb the solids distribution in the used system, making the sampling process absolutely unreliable. Thus, in the reactor used in this work, particles are suspended by producing intensive turbulence. At the same time, the use of this system allowed the comparison of the results to those obtained for settling particles. All the experiments were conducted at complete suspension which is taken to be most suitable for suspension processes from both commercial (least power consumption) and practical (maximum solids/liquid interface) viewpoints. The experiments, where the effects of impeller speed on the sample solids concentration were examined, are the only exception. Effects of Sample Tube Geometry, Location, and Sampling Velocity on Sample Solids Concentra-
5018 Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997
Figure 4. Sampling efficiency of the different probes; C h ) 5 kg‚m-3, dp ) 120/150 µm.
tion. The first series of experiments have examined the sampling efficiency of different sample tubes as a function of sampling velocity, location, and sample geometry (Figure 4). Due to the specific characteristics of solids to be suspended (very low inertia) and characteristic liquid flow in the mixing tank caused by axial mixer, the studies were carried out at three different axial positions in the mixing vessel. One sampling point was located immediately below the liquid surface (z/H ) 0.94, 1/T ) 0.09), and other two were above the impeller plane (z/H ) 0.48, 1/T ) 0.09; hereinafter, A position) and below the impeller plane (z/H ) 0.19, 1/T ) 0.09, hereinafter, B position). Due to high hydrodynamic instability of the flow in the zone close to the liquid surface, the data obtained in this sampling location are markedly unreproducible, and thus are not shown in the work. The results from other two locations are presented as a ratio of the sample solids concentration to mean solids concentration in the tank, C/C h, versus the ratio of sampling velocity to liquid velocity in the mixing tank at sampling location, vs/v0. The exact
definition of the sampling efficiency would be the ratio between the solid concentration in the sample, C, and the local concentration in the flow at the sampling point, h C0. In this work withdrawal efficiency is defined as C/C where C h is the mean concentration in the vessel. Of course this parameter is affected by the variation of the solid concentration in the vessel as a function of the spatial coordinates; however, at constant C h and stirrer speed C/C h can be used to analyze the effect of the withdrawal velocity and probe geometry. Values shown graphically are means of five runs. It must be noted that the sampling efficiency of different sample tubes were different irrespective of the fact that the sampling location and experimental conditions were the same. It is quite obvious that both the sampling velocity and sample tube geometry strongly influence sample solids concentration. All three sample tube types showed the same qualitative behavior; that is the relative sampling efficiency increases by increase in the withdrawal velocity approaching an asymptotic value. At lower velocity ratio, that is vs/v0 < 0.6, the sampling velocity influence is very pronounced but not the same for all three sampling tube types. To account for obtained results, it is necessary to relate local fluid flow velocity vector directions at selected sampling position in the tank to the sample tube geometry. Using a modified Pitot tube at both tested positions in the tank showed that the flow in the tank was markedly axial. For the achievement of the complete suspension state of the floating particles the impeller speed required is markedly higher than that for settling particles (Table 1). Therefore, the local fluid velocities are also higher and affect the particle flow more. If an L-shaped probe is used under these conditions, the direction of the fluid velocity vector is perpendicular to the suction section of the sample tube, causing insignificant deformities of fluid streamlines. In this case the solids trajectories correspond to the liquid streamlines, resulting in more solids entering this sample tube and hence higher sample solids concentration. For the blunt sample tube the fluid flow is parallel to the probe opening, and the particles have to change their direction 90° to be sampled. In this case, the geometry of the blunt probe, much more than the other two kinds of the sampling probe, changes the liquid trajectories and causes remarkable disturbances in the turbulent flow ahead of the probe. The particles of low inertia respond to the deflection of the fluid streamlines by reorienting themselves and then don’t enter the probe. As a result, the samples with lower concentrations were obtained. The 45°-edged probe is a kind of combination of the above two mechanisms of sampling, proved also in the experimental results. The sampling efficiencies of this probe at lower sampling velocities is slightly higher than those obtained by the blunt probe, but considerably lower than values obtained by the L-shaped probe. The results show that when sampling with an Lshaped probe at low sampling velocities (vs/v0 < 0.6), sample solids concentration deviation from bulk solids concentration in the mixing tank is the smallest. In addition, this sample probe is least sensitive to the changes of sampling velocity in the tested range of sampling velocities. It is quite obvious that the orientation of the suction section of the L-shaped probe is best
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suitable for markedly axial, upward fluid flow and its relatively high velocities. At higher sampling velocities, that is at vs/v0 > 0.6, the C/C h ratio approaches an asymptotic value for all three probe types. This means that at any further sampling velocity increase the sample solids concentration will not change. The results with settling particles by Kuzmanic´ et al. (1992) and Barresi et al. (1994) are consistent with results presented in this work; the sample concentration of settling particles generally reaches an asymptotic value by increasing the sample velocity (at vs/v0 > 1.1). As distinct from settling particles where obtained asymptotic values of a different sampler were significantly different (from C/C h ) 0.72 for 45°-edged probe to C/C h ) 0.89 for an L-shaped probe), in this work the differences between asymptotic values are very small, almost negligible. This observation points to an additional conclusion that at higher sampling velocities the shape of the sample tube influence on the sample solids concentration is also insignificant. In general, the asymptotic values of obtained curves for floating solids have considerably higher C/C h ratio values than those for settling solids. The results are, in the first place, due to the low inertia of suspended floating solids, resulting in very good correspondence of solid particle trajectories and the liquid of their suspension. In addition, in the field of the velocities ratio vs/v0 > 0.6, the effect of withdrawal velocity becomes more pronounced. That is why even when a blunt sampler is used, where solids should bend at a 90° angle to be sampled, the sampling efficiency is relatively high. It is quite obvious that at both sampling positions, A and B, that is above and below the impeller plane obtained dependencies of the sampling efficiencies on the velocity ratio vs/v0, are almost identical. This is primarily due to the high impeller speed required for the achievement of complete suspension state of floating suspended particles, resulting in a high degree of quality of distribution of the studied system. In this case the axial concentration gradient is, for sure, not pronounced, which was not the case in settling solids. Markedly axial fluid flow was recorded at both sampling positions in the tank, with no tangential or radial components, which might have disturbed the sampling procedure. For these solids, as well, irrespective of their very low inertia, the concentration ratio C/C h is lower than unity in the entire sampling velocity range, that is at both isokinetic and nonisokinetic conditions. This is a direct confirmation of the statement of Barresi et al. (1994), who worked with settling particles, that rather unstable hydrodynamic conditions in the mixing tank do not allow the obtainment of a representative sample. In an agitated tank, the local velocity of the fluid changes quickly, both in direction and modulus, due to the strong turbulence and periodical flow induced by the stirrer blades. Probably, the fluctuation velocities are of the same order of magnitude of mean velocities. Hence, the trajectories of the solid particles are quite complex and disordered with respect to the vectors of mean fluid velocities. Moreover, the fluid velocity field near the opening of the probe, affected by the sample probe geometry and suction flow, makes sampling even more difficult. These are the principal reasons for the decrease of sample solids concentration relative to bulk solids concentration when wall sampling is applied.
Figure 5. Sampling efficiencies for blunt tip probes of various wall thicknesses; C h ) 5 kg‚m-3, dp ) 120/150 µm.
Figure 6. Sampling efficiency as a function of vs/v0 for various sample tube inside diameters; C h ) 5 kg‚m-3, dp ) 120/150 µm.
Whitely and Reed (1959) and Belyaev and Levin (1972) studied the process of sampling from slurry pipeline walls in a solid/gas system and established that wall thickness may be one source of sampling errors. To test the effects of wall thickness in the case of sampling of floating solids from a mixing vessel, a series of measurements were performed with a straight probe made of the same material but with a different “δt” ratio of the wall thickness to inside probe diameter. As shown in Figure 5, the sampling efficiency is increased with the higher wall thickness. This is primarily the consequence of the bouncing effect. Due to specific hydrodynamic conditions during sampling, a part of the solids hit the probe wall, lose some of their inertia, and are more easily withdrawn into the sample tube. The results point to the fact that the use of the probe with the greatest wall thickness the sample solids concentration approaches the bulk solids concentration already at much lower velocities than the isokinetic one, but not exceeding the ratio C/C h ) 1 in all range of tested sampling velocities. This effect may be eliminated or minimized if a probe with very thin and sharpened walls is used. Unfortunately, thin probe walls are very liable to damages in systems with firm particles due to intensive suspension flow and hardness of suspended material. Apart from the wall thickness effects, the changes in the concentration ratio C/C h affected by the sample tube hole diameter were also examined (Figure 6). Three straight probes with different hole diameters, 4, 6, and 8 mm, were used. Higher concentrations are obtained
5020 Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997
with a larger sample tube. This behavior has to be related to the Reynolds number in the sampling tubes. It is known that this dimensionless number ()vsφ/ν) presents the ratio of the inertia forces to the viscous forces in the flow. For one constant value of the withdrawal velocity, the Reynolds number increases by increasing the inside diameter of the tube. In this case the inertia forces are being more dominant and therefore more solids enter the sample tube. Effect of Slurry Characteristics and Mixing Velocity on the Sampling Efficiency. A number of authors have already shown that the sampling efficiency depends, to a considerable extent, upon the particle inertia. Namely, if the densities of two present phases are significantly different, the inertia of particles will differ in relation to an equal volume of the surrounding fluid. Frequently, particle motion does not follow the fluid streamlines, particularly if it changes its direction significantly. Therefore, it is very important to establish to what extent the sampling procedure affects changes in fluid flow and how the particles respond to these disturbances. Particles response is a function of inertia parameter and is defined as
K)
Fpd2v0 18µL(φ/2)
(2)
This dimensionless group is known varyingly as the Stokes or Bart number, where d is the particle size, v0 is the local fluid velocity, φ is the sample tube inside diameter, µL is the fluid viscosity, and Fp is the solids density (Nasr-El-Din et al., 1996). It must be noted that in the numerator of this dimensionless group the square of the suspended solids diameter is present. This points to the conclusion that this parameter strongly affects the particle inertia and should, therefore, affect the sampling efficiency. Therefore, the effect of the floating particle size on the sample solids concentration was also studied. Particles of three different sizes were examined. The results of examination are given in Figures 7a and 7b as the relation between sampling efficiency C/C h and velocity ratio vs/v0, showing that particle size, in the examined particle size range, does not affect the sampling efficiency. This conclusion was confirmed at both sampling positions, A and B. It should be kept in mind that Stokes number, defined by eq 2, was formed on the basis of work with settling particles. For floating particles, however, some modifications of Stokes number would be necessary, taking into account a pronounced effect of the buoyant force in the system. To confirm these observations, further research would be necessary. As distinct from the floating particle size, the mean bulk solids concentration in the mixing tank affects the sampling efficiency. This is confirmed by the results shown in Figure 8. Tested concentrations were in the range of 5-10 kg‚m-3. Sampling was always performed at the same stirrer speed, NJS ) 730 rev‚min-1, since it was established that the bulk solids concentration has negligible effect on minimum stirrer speed (Table 1), as shown by Joosten et al. (1977). Sampling errors seem to decrease with increasing bulk solids concentration due to the fact that with the concentration increase the number of solids is increased so that the drag forces of the withdrawal flow are more efficient. In general, the impeller speed is one of the most important parameters for solids suspension. Actually, suspended particles follow the fluid streamlines, that
Figure 7. Effect of particle size on sampling efficiency at two sampling positions in the mixing tank; C h ) 5 kg‚m-3.
Figure 8. Dependence of the sampling efficiency on mean slurry concentration; dp ) 120/150 µm.
is move at the same speed as the surrounding fluid. If either the direction or magnitude of fluid velocity changes, the solids will respond by reorienting themselves. This results in changes of local solids concentrations. In this work, the sampling efficiency of a straight sample tube was examined at three impeller speeds. The first run was carried out at N ) NJS ) 730 rev‚min-1, that is at the speed required for the just-suspended state, and the other two at 803 rev‚min-1 (N/NJS ) 1.1) and 876 rev‚min-1 (N/NJS ) 1.2). Figure 9 shows that the sample solids concentration was higher in samples obtained at higher impeller speeds. However, in this case, the differences in the sampling efficiency are due to different degrees of
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quality of distribution of the solid particles in the mixing tank directly affected by hydrodynamical conditions in the mixing tank. These results point to some very important conclusions, particularly from the wall sampling standpoint. With increased impeller rotational speed (N/NJS ) 1.2) and using a thin wall sampler (δt ) 0.125), it is possible to obtain a representative sample at isokinetic sampling conditions. With respect to the fact that power consumption is increased in this case, it should be attempted to find some optimum conditions both from the sampling procedure and economic viewpoints. Theoretical predictions of sample solids concentration from a mixing tank are very difficult. As can been seen, sampling efficiency deviates from unity, and these deviations depend on the inertial effects, velocity ratio, the geometry of the sampling device, and the physical properties of the solids and the fluid. The calculation of the sampling efficiency would require three basic steps: establishment of the flow pattern upstream of the sampler, determination of the particle trajectories, and calculation of the sampling efficiency from the limiting particle trajectory. However, in mixing tanks, predicting the flow field ahead of a sampling probe is so complex. First, fluid dynamics of turbulent flow in mixing tanks are not fully understood. Although various turbulence models have been employed in the literature, some adjustments for the boundary conditions at the impeller edge have always been necessary (MacTaggart et al., 1993). Also, complications to the fluid flow that result from the addition of solids would occur. Moreover, dynamics of sample withdrawal together with fluid-particle dynamics within the tank render the sample withdrawal a challenging problem to solve.
tube affect the sampling efficiency. Sample tube geometry has no particular effect on the sampling efficiency at increased sampling velocity (vs/v0 > 0.6). 2. The sampling efficiency is markedly a function of the sampling velocity. This is particularly pronounced if the sampling velocity is lower than the local fluid velocity. With the sampling velocity increase, the C/C h concentration ratio gradually increases to approach an asymptotic value. Accordingly, sampling efficiency does not depend on the sampling velocity for vs/v0 > 0.6. An L-shaped sampler is a lot less sensitive to varying sampling velocity. Using this type of probe, the sample solids concentration shows the least deviation from mean solids concentration in the mixing tank at low sampling velocities. 3. The probe wall thickness may cause deviation of the sample solids concentration from the bulk solids concentration, due to the bouncing effect. A part of the solids that impinge upon the wall of the sampler and lose a part of their kinetic energy are more easily withdrawn into the sample tube, causing an increase in sample solids concentration. 4. The sample tube diameter is one of the parameters affecting the sample solids concentration. The sample solids concentration is increased with larger sample tube diameter. This behavior can be related to the Reynolds number, that is the pronounced effect of inertia force in the sample tube. 5. In the tested range of particle size, the particle diameter was found not to affect the sampling efficiency. This is most likely due to the pronounced effect of the buoyant force on the examined system. To confirm this conclusion, further research would be necessary. 6. The sample solids concentration increase by increasing the bulk solids concentration in the tank. Taking into account that the bulk floating solids concentration has negligible effect on NJS, the result presented is a consequence of an increase in the drag force exerted by the fluid on the particles, thus increasing the tendency for particles to follow the fluid flow into the sample tube. 7. The sampling efficiency changes with the variation of the impeller speed. In fact, varying the impeller speed alters the local solids concentration, i.e., a degree of quality of solids distribution in the tank. Therefore, the values of sampling efficiency obtained at different impeller speed cannot be compared. 8. At complete suspension state it is practically impossible to obtain a representative sample of floating suspended particles from a mixing tank with markedly axial flow using the wall sampling technique. This is probably due to very unstable hydrodynamics in the mixing tank. An ideal sample may be obtained by appropriating operating conditions (e.g., higher impeller speed). However, all the conclusions point to the fact that this method may be applied in practice with extreme caution.
Conclusions
Acknowledgment
The following conclusions may be drawn from the results of wall sampling experiments with suspended floating solids: 1. The shape of a sample tube strongly affects the sample solids concentration obtained by the wall sampling technique. Namely, a sample tube shape causes quite specific hydrodynamics ahead of it. This effect as well as the relationship between the directions of the fluid velocity vector and suction section of the sample
The sponsor of our research is The Ministry of Science and Technology of the Republic of Croatia.
Figure 9. Effect of impeller speed on the sampling efficiency; C h ) 5 kg‚m-3, dp ) 120/150 µm.
Nomenclature B ) baffle width, m C ) sample solids concentration, kg‚m-3 C h ) bulk solids concentration, kg‚m-3 C0 ) local solids concentrations, kg‚m-3
5022 Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 d ) particle diameter, m D ) agitator diameter, m FrJS ) Froude number to just-suspended particles off surface vessel H ) height of liquid from bottom of vessel, m k ) constant in eq 1 K ) particle inertia parameter l ) length of sample probe, m N ) impeller speed, rev‚min-1 NJS ) impeller speed to just-suspended particles, rev‚min-1 T ) vessel diameter, m vs ) sampling velocity, m‚s-1 v0 ) local fluid velocity in the vessel, m‚s-1 z ) axial sampling position from the bottom, m δt ) relative sample tube wall thickness (wall thickness/ inside diameter of probe) φ ) sample tube inside diameter, m FL ) density of liquid, kg‚m-3 Fp ) density of particle, kg‚m-3 ∆F ) density difference between liquid and solid, kg‚m-3 µL ) viscosity of liquid, N‚s‚m-2
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Received for review March 11, 1997 Revised manuscript received July 7, 1997 Accepted July 8, 1997X IE970201K X Abstract published in Advance ACS Abstracts, September 1, 1997.
