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Enhancement of Colloidal Filtration: A New Combined Approach Based on Cake and Suspension Destabilization Sasanka Raha,† Pradip,† Prakash C. Kapur,† and Kartic C. Khilar*,‡ Tata Research DeVelopment and Design Centre, 54B Hadapsar Industrial Estate, Pune - 411013, Maharashtra, India, and Department of Chemical Engineering, Indian Institute of Technology, Bombay, Mumbai-400076, Maharashtra, India
Pressure and vacuum filtration experiments using A16SG alumina with and without homogenization of formed cake and suspension are carried out. Homogenization involving mixing of formed cake with the suspension on top of the cake enhances filtration process performance in terms of reduction in filtration time without any alteration in the equilibrium solids volume fraction. A model is developed and validated based on the MeanPhi model of pressure filtration to simulate the filtration behavior in the presence of continuous and intermittent homogenization. It is demonstrated that a single batch pressure filtration experiment is sufficient to provide the necessary information to simulate an enhanced pressure filtration process involving homogenization. Simulations for situations involving increasing numbers of homogenization and continuous homogenization are also carried out. Advantages regarding time and equilibrium solids fraction can be availed where homogenization along with change in the state of suspension aggregation by using additive(s) or pH change is carried out. Under such a scheme, a filtration process should start with a flocculated/aggregated condition along with mixing. With progress of the process, the suspension should be gradually converted to dispersed type by modulating the slurry chemistry, to achieve a maximum equilibrium solids volume fraction. Introduction Cake filtration is a widely used unit operation to separate solid from liquid. Similar to many other industrial processes, productivity and product quality are critical issues in the filtration process. There are different chemical and physical methods available to enhance the performance of filtration process. For example, the process of chemically modifying the rheological behavior of the slurry by adding additives to modulate the filtration process is well recognized to enhance the performance of filtration processes.1-6 Dispersion of a colloidal system usually leads to long filtration time but provides the advantage of a high equilibrium solids volume fraction (low cake moisture). On the other hand, flocculation leads to rapid filtration with the penalty of higher cake moisture. It is critical to assess the extent of moisture removal along with the filtration time, as it is observed that it is not easy to improve the extent of dewatering and the kinetics of the filtration process simultaneously in batch filtration carried until equilibrium by dispersion and flocculation of colloidal systems.7 One physical route for enhancing the performance of the filtration process is to follow methodologies in which cake formation over the membrane is prohibited. In cross-flow filtration technology, the tangential movement of the suspension over the medium hinders the cake formation. Hence, the separated solids remain in the suspension without forming a layer of solids on the filtering surface. There are approaches involving backwashing that increase flux of the filtration system in ultrafiltration and cross-flow microfiltration.8-10 The literature also contains approaches to enhance the performance of crossflow filtration process by design modifications, such as, addition of baffles, membrane vibration and/or shearing, maintaining oscillatory flow in the channel, and application of ultrasound, electricity, air sparging, and so on.11-18 Besides cross-flow * To whom correspondence should be addressed. E-mail: kartic@ iitb.ac.in. † Tata Research Development and Design Centre. ‡ Indian Institute of Technology.
filters, recent efforts have been taken to design and fabricate a cakeless continuous filtration system by using rotating disk filtration.19 In spite of the efforts for fabrication and design of cakeless continuous filtration systems, there is no published experimental and modeling study on cake filtration performance enhancement for laboratory scale batch filtration, although batch filtration trials are traditionally carried out to design, scale up, and understand any filtration operation. Although it is understood that the absence of formed cake over the medium leads to reduction in filtration time, there is no published experimental or modeling effort involving cake filtration process under homogenization. This study is taken up to fill this gap and develop a simple engineering model to simulate enhancement in the filtration process and validate the model with experimental data involving enhancement in cake filtration processes. In this work, modeling and experimental investigation for filtration with and without suspension homogenization is carried out. We have also studied the improvement in filtration process performance when the chemistry of the suspension is modulated during the filtration process along with suspension homogenization. Pressure filtration has been studied for past many decades to various levels of experimental and modeling details.20-31 It is known that pressure filtration has two stages, namely, the cake formation and consolidation stages.22,24 Conventional filtration models21,27 deal with the cake formation stage. Implementation of advanced, rigorous models based on continuity and momentum balance equations requires a complex numerical procedure.22,24 These model equations have material independent components in addition to material dependent constitutive properties, namely, compressibility and permeability (or a hindered settling function). Estimation of constitutive properties from these comprehensive models is a difficult task,26,31 even though it is necessary for simulation activity. A simple engineering model is needed which is capable of estimating the constitutive properties and simulating cake formation and consolidation stages under diverse physicochemical process conditions. Considering the complexity of the advanced rigorous
10.1021/ie801750w CCC: $40.75 2009 American Chemical Society Published on Web 07/02/2009
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Table 1. Different Types of Filtration Experiments filtration methodology
pressure
vacuum
without homogenization (conventional) with homogenization (one time) with homogenization (continuous) with homogenization and change in pH (one time)
P1 P2
V1 V2
P3
models in simulating the filtration process, we start with the easy to implement and widely validated engineering model for filtration, namely, the Mean-Phi (MP) model for cake formation and consolidation,25,28 and develop an extended M-P model to simulate enhancement of the filtration process by cake and suspension homogenization. Development of extended M-P model is described in the Appendix. Experimental Section Particulate suspensions for filtration tests were prepared from A16 SG alumina (supplied by Alcoa, USA) having a 9.3 m2/g BET surface area and 0.4 µm mean particle size, as measured by a Horiba laser scattering particle size analyzer. The point of zero charge (pzc) for this powder was determined to be at pH 6.5 by electrokinetic measurements using a Zetameter 3.0. Filtration test work involved pressure filtration (P1) carried out in a highly instrumented and programmable computer driven laboratory scale test rig with cell diameter of 0.04 m (described in detail by its designers31) and vacuum filtration (V1) using a Buchner funnel (a funnel of 0.095 m internal diameter) under 300 mm Hg vacuum. Whatman filter paper no. 42 was used as the filter medium in both pressure and vacuum filtration setup. We prepared the suspensions of A16 SG alumina powder by adding a known quantity of powder in water. The suspension was conditioned with a magnetic stirrer for 2 min. If required, pH was adjusted during conditioning with 4 kmol/m3 HNO3 or 4 kmol/m3 NaOH solution. The suspension was next dispersed using a sonicator (Branson Model 450, USA) for 2 min using 50% duty cycle and a power input of 40 W. The initial solids volume fraction was calculated from the weights of powder and liquid taken to prepare the slurry and specific gravity of the material. The initial slurry height was computed from the weight of slurry filled in the filtration chamber, knowing the cell diameter. The average solids volume fraction (φ) in the cell was calculated using the volume of filtrate data as a function of time. Different types of filtration experiments that were carried out in this study using A16SG alumina suspension are presented in Table 1. Experiments for Enhancement of Filtration with Homogenization Our earlier work indicated that the volume of filtrate expelled from the filtration cell per unit time decreased as a function of time since the cake formed during the process provided additional resistance to continuation of fluid flow. Therefore in order to enhance the filtration rate during the latter part of the filtration cycle, we thought of breaking this barrier. We stopped the filtration experiment midway and homogenized the cake with the residual suspension in the cell. As hypothesized through this process, we could enhance the filtration kinetics and hence prove the concept. The homogenization was carried out either by stirring with a spatula for 1 min in the case of pressure filtration (P2) followed by re-pressurizing the cell and continuing
Figure 1. Reproducibility trial shown for filtration of A16 SG alumina in pressure filtration.
the experiment further or by continuous mechanical stirring of the suspension during the vacuum filtration experiment (V2). Experiments for Enhancement of Filtration with Homogenization and Change in pH We have earlier reported that alumina suspensions are dispersed in an acidic pH range (for example, pH 3.3 or 4.5) as opposed to being in an aggregated state at its natural pH (8.5).30 Accordingly, the kinetics is slower at acidic pHs even though the equilibrium moisture content of the cake (end moisture content) is lower as compared to natural pH. In order to take advantage of both the faster kinetics at natural pH and achieving lower end moisture content in the cake at acidic pHs, we thought of starting the experiment at natural pH (faster kinetics) and changing the pH midway along with homogenization in order to achieve lower end moisture content. This is what we did in experiment P3. In this case, batch pressure filtration of A16 SG alumina suspension of pH 8.5 was carried out for 900 s (well before the equilibrium solids volume fraction is reached) under 20 kPa pressure. The pressure filtration cell was then opened, concentrated acid was added drop-by-drop to the suspension so as to achieve the desired acidic pH, and homogenized with the help of a spatula for 30 s. The suspension is then taken out of the cell, ultrasonicated for half minute, and taken back to the cell again. The pH of the homogenized mixture is measured to be 4.4. The cell was closed, and pressure filtration of the suspension was continued at the same pressure until the end point. Results and Discussions A typical filtration test involves repeating the experiment at least twice. The reproducibility of our experimental results is illustrated in Figure 1 for a typical batch pressure filtration experiment (P1) using A16 SG alumina suspension at pH 9.3, at a pressure of 100 kPa, for an initial slurry height of 0.015 m in filtration chamber, and at an initial solids volume fraction of 0.1. Figure 2 compares the experimental observations for pressure filtration of A16 SG alumina with two different routes namely conventional batch filtration with (P2) and without suspension homogenization (P1). It shows the filtration of A16 SG alumina under a pressure of 20 kPa at pH 8.5. Homogenization was carried out at 800 s after starting the filtration experiment. After homogenization, again the filtration was continued until completion. As expected, homogenization midway during the experi-
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Figure 4. Advantage in filtration time obtained in vacuum filtration because of continuous suspension homogenization in a Buchner funnel.
Figure 2. Experiments and simulation of filtration behavior with intermediate suspension homogenization.
Figure 3. Simulation of filtration behavior with multiple suspension homogenizations.
ment lead to reduction in filtration time from approximately 1500 to 1200 s, even though there was identical equilibrium solids volume fraction in the cake at the end of the two experiments. In other words, we have been able to enhance filtration kinetics while keeping the end moisture content at the same level. We have also simulated this experiment with the help of our extended M-P model (details are provided in the Appendix). It is important to determine at what time during the test the homogenization should be done. With the help of our model, we have been able to simulate the effect of the time at which homogenization is invoked, as well as how many times it is performed on the filtration behavior. From Figure 3, it is observed that with increasing number of homogenization steps, the filtration time required to achieve the same equilibrium solids volume fraction decreases. These simulation results clearly demonstrate the benefit of homogenization in enhancing filtration kinetics yet achieving the same end point moisture content. The results also suggest that the effect is more pronounced if the homogenization is carried at an early stage. We have estimated the resistance of filter paper (along with the sintered disk of the pressure filtration setup) by passing water through it at 20 kPa. The total medium resistance to water flow in the pressure filtration setup is estimated to be 2 × 1010 1/m. The actual resistance during the pressure filtration process might be higher than this estimated resistance because the filter papers
may get clogged by particles. The medium resistance can be used to estimate the theoretical lower limit of the time requirement of the filtration process. Simulation results, for example, under continuous homogenization with medium resistances of 2 × 1010 and 2 × 1011 1/m are also shown in Figure 3. The filter medium resistance dictates the lower time limit in the case of continuous homogenization. In the batch pressure filtration cell, it was difficult to carry out continuous homogenization because of the absence of continuous stirring facility in our pressure filtration set up. We therefore conducted the filtration test with continuous homogenization using a stirrer on top of our Buchner funnel vacuum filtration setup. The vacuum filtration (with and without continuous homogenization, i.e. V1 and V2) of A16 SG alumina suspension at pH 8.5 under 300 mm Hg vacuum is shown in Figure 4. Unlike one time homogenization in pressure filtration (Figure 2), Buchner funnel homogenized filtration involves continuous agitation and homogenization leading to significant reduction in filtration time. The filtration time to achieve the same end moisture content is reduced by 50%. We have thus demonstrated the effect of homogenization on filtration kinetics. Similarly, one can reduce the end moisture content by changing the state of aggregation/dispersion of suspensions being filtered. For example, the end moisture content is highest near the pH, pzc of A16 SG alumina.30 One can therefore reduce the end moisture content of the cake if the pH is changed during the filtration process. We have confirmed this hypothesis by conducting experiments where the pH was changed midway during the experiment. The results of the experiments designed to confirm the effect of changing the pH midway during filtration (P3) are presented in Figure 5. The results of conventional pressure filtration experiments (P1) carried out with A16 SG alumina under 20 kPa at pH conditions of 8.5 and 4.5 are also shown in the same figure. The remarkable effect of pH on kinetics of filtration should be noted. The end moisture content at pH 8.5 is significantly higher (solids volume fraction is around 0.41) as compared to that at pH 4.5 (solids volume fraction of about 0.7). We started the filtration test at pH 8.5 and changed the pH to 4.4 (900 s after starting the experiment), homogenized the suspension, and continued filtration (experiment P3). We were able to achieve a solids volume fraction of 0.54 while the kinetics was comparable to that observed at pH 8.5. The clear advantage of changing pH midway during the filtration test is thus demonstrated even though the final moisture content is not identical to what we would have achieved had we started the filtration at pH 4.4 only (the kinetics of course is much slower). As illustrated in Figure 5, the relatively dispersed slurries (at pH 4.5, d50 of 0.6 µm) exhibit slower filtration kinetics, but
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3.3 at that solids volume fraction. Conventional filtration at pH 3.3 does have the advantage of high equilibrium solids volume fraction (low moisture content of the cake) but at the cost of achieving it at 7500 s of filtration. On the other hand, our simulation results indicate that by changing the pH to 3.3 after 300 s of filtration, one can achieve the same end moisture content at about 3000 s (a 50% decrease in the time of filtration). Conclusions
Figure 5. Experimental result on advantage with intermediate slurry modification and homogenization over conventional filtration.
Our experimental and modeling work reported in this communication has demonstrated that to maximize equilibrium solids volume fraction with minimum time of filtration, it is desirable to have an equipment/process which has the ability to change the state of aggregation midway during the filtration process. From the point of view of better filtration behavior, a filtration cycle should be designed in such a way that it starts with suspensions under aggregated conditions (faster kinetics) and then gradually changes to fully dispersed conditions toward the end of the process. This process may be termed as filtration under dynamic slurry chemistry conditions that gives the advantage of faster kinetics and at the same time lower end moisture content (high equilibrium solids volume fraction). Acknowledgment We gratefully acknowledge the financial support that was provided for this work by the Department of Science and Technology (DST), Govt of India. The authors are grateful to TRDDC Management for encouragement and support. Appendix
Figure 6. Advantage with intermediate slurry modification and homogenization over conventional filtration.
lower moisture content (higher solids volume fraction) in the final cake as compared to aggregated slurries (at pH 8.5, d50 of 2 µm). The dispersed particles tend to pack better than aggregated particles.30 The aggregates tend to lock up water and therefore increase the moisture content of the final cake. Moreover, the dispersed particles typically have a much wider size distribution than aggregated particles and hence tend to pack better. The larger size of the aggregates leads to relatively faster filtration. In the intermediate case, that is, starting at pH 8.5 and changing the pH to 4.5 midway in the experiment, we can speculate that the situation with respect to kinetics and final moisture content will be somewhere in between the extremes. This is indeed the case. The advantage obtained by homogenization and modification of the state of aggregation (by pH change at an intermediate level) has also been simulated by us (see the Appendix for details). The results are presented in Figure 6. Using the experimental filtration data and estimated M-P model parameters for filtration of A16 SG alumina under two different pH conditions (pH 7.6 and 3.3), simulation is carried out for filtration with homogenization and slurry modification (change in pH). The simulated filtration behavior in Figure 6 is shown for the case when filtration is carried out at pH 7.6 for 300 s followed by homogenization and slurry modification to pH 3.3. We have assumed for the purposes of simulation that after homogenization and pH change to 3.3, the suspension attains similar state of aggregation as that of fresh suspension of pH
We have earlier developed and validated the M-P model for P1 and V1 type of filtrations for a wide range of physical and chemical process conditions.28 In this work, we extend the M-P model to simulate a filtration process involving homogenization. Cake Formation Model for Intermediate Homogenization. For simulation purposes it is considered that each intermediate homogenization properly mixes the cake and suspension above the cake to form a homogenized suspension. We consider that the initial solids volume fraction of the suspension is φ0, the transition solids volume fraction between cake formation and consolidation is φc, and equilibrium solids volume fraction is φ∞ in a filtration process. In conventional filtration without intermediate homogenization, the average solids volume fraction in the filtration cell increases from φ0 to φc during cake formation followed by φc to φ∞ during consolidation. We consider stagewise filtration when intermediate homogenization is carried out N number of times (that is, stage 2 to stage N + 1 of Table A1) during enrichment of the solids volume fraction from φ0 to φc. Hence, we consider that homogenization is done when the overall solids volume fraction reaches φ1, φ2, φ3, ..., φN. Table A1. Stagewise Filtration with Intermediate Homogenization During Cake Formation stage
initial solids volume fraction in a stage
end solids volume fraction in a stage
filtration time in a stage
1 2 ... N N+1
φ0 φ1 ... φN-1 φN
φ1 φ2 ... φN φc
t1 t2 ... tN tN+1
In the stagewise filtration process, total cake formation time is given as
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tc ) t1 + t2 + t3 + ... + tN+1
(A1)
From the analogy of the M-P model for cake formation,28 the filtration time required for the i-th stage is given as ti )
hi-12 βi-1
2
[
1-
]
2
φi-1 φi
for i ) 1, 2, ..., N
(A2)
Where, hi-1 and φi-1 represent suspension height and average solids volume fraction at the beginning of the i-th stage in stagewise filtration. Recognizing the fact that the solids volume fraction at the end of the N + 1-th stage is φN+1 () φc), the time required for the N + 1-th stage is given as tN+1 )
hN2 βN
2
[
1-
φN φc
]
(φc - φi-1)(1 - φc)3 φi-1φc2
∆Pf,c dV ) dt ηRc
∆Pf,m dV ) dt ηRm
(A3)
for i ) 1, 2, ..., N + 1 (A4)
Where βi2 represents the specific filtration rate parameter for the i-th stage, k represents the lumped permeability factor that includes specific surface area, tortuosity, and fluid viscosity. In formulating the above equations, it is assumed that k and φc are independent of the homogenization stage concerned, that is, independent of the initial solids volume fraction of suspension. We will justify this assumption based on our observations in the Simulation Methodology section. Cake Formation Model for Continuous Homogenization. It is considered that continuous homogenization is carried out while the average solids volume fraction increases from φ0 to φc. We consider that, during continuous homogenization, there is no cake formation above the medium and hence the filter medium resistance controls the fluid flow through the medium. Above φc, both medium and the consolidating cake offer resistance to liquid flux. During homogenization,
(A8)
where ∆Pf,c represents pressure drop across the cake in fluid phase and Rc represents the cake resistance. Also, from fluid flow considerations through the medium, we can write
2
Following the analogy to M-P model development, βi2 is represented as28 βi2 ) 2k
such considerations, we do not have separate cake consolidation models with and without homogenization. Considering medium resistance to be nonzero, we now develop the consolidation equation. During consolidation, the liquid flux through cake is written as
(A9)
where ∆Pf,m represents pressure drop across the medium caused by fluid flow through the medium. Following the analogy of eq B16 (of ref 30), eq A8 is rewritten as dV ) dt
∆Pf,c h k(1 - φ)3 φ2
(A10)
where h and φ represent cake height and average cake solids volume fraction at any instance during consolidation. Total pressure drop across the cake is written as ∆Pc ) ∆P - ∆Pf,m
(A11)
Within the consolidating cake, stress is distributed between the solid and fluid phases. It is assumed in the M-P model that the fluid stress drops linearly with average solids volume fraction,28 φ. With similar consideration of stress distribution between the fluid and solid across the cake, we get ∆Pf,c )
φ∞ - φ ∆P φ∞ - φc c
(A12)
Combining Equations A11 and A12, we get ∆P dV ) dt ηRm
(A5) ∆Pf,c )
where V is cumulative specific filtrate volume at time t, ∆P is applied pressure difference, η is filtrate viscosity, and Rm is medium resistance. From a volume balance, we have h0φ0 dφ dV ) 2 dt φ dt
(A6)
Combining eqs A5 and A6 and integrating, we get ∆P 1 1 - ) t for φ0 e φ e φc φ0 φ ηRmh0φ0
(A7)
Cake Consolidation Model. During consolidation, only the consolidating cake layer exists and there are no separate layers of cake and suspension. Hence, there is no utility of homogenization during cake consolidation. Also, it needs to be understood that mechanical agitation and mixing of the consolidating cake with high solids volume fraction is difficult. With
φ∞ - φ (∆P - ∆Pf,m) φ∞ - φc
During consolidation, hφ ) h0φ0
(A13) (A14)
Combining eqs A9, A10, A13, and A14, we get k∆Pφ2(φ∞ - φ)(1 - φ)3 dφ ) dt h0φ0[(φ∞ - φc)h0φ0φ + kηRm(φ∞ - φ)(1 - φ)3] for φc e φ e φ∞ (A15) Hence eq A15 is the consolidation equation in the presence of medium resistance. It needs to be noted that for Rm ) 0, eq A15 is transformed into the M-P model consolidation equation (eq 17 of ref 28). This suggests that eq A15 is a more generalized consolidation equation. Simulation Methodology. We carry out pressure filtration (P1) of A16 SG alumina at pH 9.5 using varying initial solids volume fraction (φ0) in the range of 0.03-0.3 under 100 kPa applied pressure and apply the M-P model to estimate three
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Figure A1. k, φ∞, and φc as a function of initial solids volume fraction, φ0.
model parameters, namely k, φc, and φ∞. The implementation of the M-P model requires knowledge of three process parameters: k, which is common to cake formation (stage 1) and cake consolidation (stage 2); φc, which lies at the junction of these two stages; and φ∞, which determines the equilibrium solids volume fraction at the end of the process. These parameters are estimated by fitting stage 1 and stage 2 equations of the M-P model to experimental data by minimizing a sum of the squares of errors in a nonlinear optimization scheme called SUMT. Once these three parameters are obtained, βm2 and the critical time (tc) are obtained by using eqs 13 and 14 (of ref 28). Figure A1 shows the effect of varying the initial solids volume fraction (φ0) on the M-P model parameters for A16 SG alumina at 100 kPa at pH 9.5. The gel point (φg) as measured by a batch settling trial for A16 SG alumina is known to be 0.054.28 From Figure A1, we observe that the values of the parameters (k, φc, and φ∞) are substantially low below the gel point (that is, when φ0
