Enhancing Impeller Power Efficiency and SolidâLiquid Mass Transfer

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Enhancing impeller power efficiency and solid-liquid mass transfer in an agitated vessel with dual impellers through process intensification Daniel Stoian, Nicky Eshtiaghi, Jie Wu, and Rajarathinam Parthasarathy Ind. Eng. Chem. Res., Just Accepted Manuscript • Publication Date (Web): 25 May 2017 Downloaded from http://pubs.acs.org on May 27, 2017

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Industrial & Engineering Chemistry Research

Enhancing impeller power efficiency and solid-liquid mass transfer in an agitated vessel with dual impellers through process intensification Daniel Stoian1, Nicky Eshtiaghi1, Jie Wu2 and Rajarathinam Parthasarathy1* 1. Chemical & Environmental Engineering, School of Engineering, RMIT University, Melbourne, 3000, Australia 2. Fluids Engineering Laboratory, Mineral Resources Flagship, CSIRO, Building 121, Bayview Avenue, Clayton, Vic, 3168, Australia

*Corresponding author. Tel.: +61 3 9925 2941; E-mail address: [email protected] Postal address: Chemical and Environmental Engineering, School of Engineering, RMIT University, City Campus, Melbourne VIC 3000, Australia

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Abstract The effects of high volumetric solids concentration (CV), impeller type, and baffles on the impeller power input required for solids suspension and dispersion, and the solid-liquid mass transfer coefficient (kSL) were studied in this work using an agitated vessel with dual impellers for the purpose of process intensification. It was found that at CV = 0.2 (v/v), the impeller power consumption required for solids suspension per unit mass solids (εJS = PJS/MS) is minimized while at the same time achieving maximum kSL values. Overall, it was observed that process intensification could be achieved using two radial flow impellers in a taller vessel under unbaffled conditions. A case study highlighting the benefits of adopting some of this study’s recommendations is presented. Mathematical correlations proposed to estimate εJS, impeller power consumption for solids dispersion and kSL as a function of CV were found to fit experimental data reasonably well.

Keywords Process intensification, Zwietering correlation, solids suspension, solid-liquid mass transfer, dual impeller, baffling


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1. Introduction Mechanically agitated vessels are widely used in process industries to achieve suspension of solids in liquid for interphase mass transfer operations such as leaching, crystallization, adsorption and solidcatalysed reactions. The mass transfer efficiency is dependent on the chemical and physical properties of the materials and the efficient use of the vessel. Due to increasing financial constraints, industries now demand an intensification of existing processes to achieve increased production rates. Process intensification in solid-liquid agitated vessels has been recently shown to be achieved by operating them at higher solids concentration.1 However, changing operating parameters such as solids concentration or equipment size and its layout will influence parameters such as the impeller power consumption and solid-liquid mass transfer coefficient (kSL). An important parameter that determines the efficiency of solid-liquid agitated vessels is the critical impeller speed to ‘just suspend’ all particles, which is denoted as NJS. Zwietering2 defined NJS as the impeller speed at which no particles remained stationary at the vessel bottom for more than 1 or 2 seconds and derived the following correlation to predict NJS: = .

. . . .

(1)

where S is a constant based on impeller type, impeller diameter, and off-bottom clearance, ν is the kinematic viscosity (m2/s), g is the gravitational acceleration constant (m/s2), ρS and ρL are the densities of the solid and liquid phases, respectively (kg/m3), dp is the particle diameter (m), D is the impeller diameter (m), and X is the ratio of mass of solids to mass of liquid. The value of S and the exponents in the equation were determined by regression analysis. Though many others have proposed correlations to determine NJS after Zwietering,3-5 Zwietering’s correlation is the most widely used and tested one and therefore is the only one discussed in this paper. Zwietering’s correlation is purely empirical. While a few other studies have largely corroborated Zwietering’s findings,6-8 others have identified conditions at



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which the correlation is not reliable. Choudhury9 pointed out that Zwietering’s equation is not reliable for solid-liquid systems with solid loadings greater than 0.15 (v/v). Myers et al.10 examined the effect of solid loadings on NJS and found that the exponent on X increased with increasing solids concentration from 0.097 at 5 wt% to 0.34 at 40 wt%. Thus, it is clear that the validity of Zwietering’s correlation is untested for high solids concentrations. As recent studies have shown that operating solid-liquid agitated systems at higher solids concentration (> 0.20 (v/v)) achieved greater energy efficiency,11-13 determining the reliability of Zwietering’s correlation in such systems would be useful for design purposes. The effect of geometry is accounted for by the constant, S and the impeller diameter, D in Zwietering’s correlation. Especially, S is a function of impeller type and diameter, and its off-bottom clearance. The possible combination of these parameters is infinite. In addition to Zwietering, other researchers have also reported S values for a wide range of impeller and tank geometries.14-17 However, a majority of these studies were confined to baffled vessels. Therefore, the reliability of Zwietering’s correlation in determining NJS in unbaffled vessels is still unclear. Moreover, information is scarce on the reliability of Zwietering’s correlation for solid-liquid agitated systems with multiple impellers. Mak8 reported that NJS for a solid-liquid agitated system fitted with a second impeller decreased or increased depending on impeller spacing due to the degree of interaction between liquid flows generated by the upper and lower impellers. Dutta and Pangarkar18 studied the effect of multiple impellers on NJS in baffled vessels where the number of impellers was equal to the ratio of liquid height to vessel diameter. They concluded that Zwietering’s correlation could be used to predict NJS in multiple impeller systems though with some changes in the exponents. However, they did not report any S values for their system. Also, there is a lack of information on the suitability of Zwietering’s correlation to unbaffled vessels fitted with multiple impellers. Reporting impeller speed rather than the impeller power consumption for the complete suspension of solids does not allow the comparison of energy efficiency reported in different studies.19 Therefore, it is


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highly desirable to compare solid-liquid mixing systems on the basis of specific impeller power consumption at NJS to identify efficient processes. Many investigators reported specific impeller power input on the basis of vessel volume.11, 20 Drewer et al.,21 on the other hand, proposed specific power input on the basis of the mass of solids suspended stating that the rate of reaction or mass transfer is independent of a further increase in agitation or vessel volume once off-bottom solids suspension is achieved. They found that when the specific power consumption at NJS per unit mass of solids suspended (PJS/MS) is plotted against the solids concentration, the curve on the graph had a minimum value around a solids concentration of 0.30 (v/v). Similar findings were observed by Raghava Rao et al.,7 who found that PJS/MS decreased with increasing solids concentration. Subsequent studies by researchers using this concept found that, in PJS/MS versus solids concentration plots, a minimum value for PJS/MS occurs at around a solids concentration of 0.20 (v/v) and therefore a significant energy savings can be achieved by operating solid-liquid agitated systems at this solids concentration because more solids can be suspended per unit power input.12, 19, 22 Researchers have studied various ways of minimizing impeller power consumption in solid-liquid agitated systems by investigating different impeller or vessel geometries. It is well established that lower power number impellers such as A310 are more economical in baffled vessels in achieving NJS.17,

23

However, a higher power number impeller such as the Rushton turbine was reported to be more energy efficient in unbaffled vessels.19, 24, 25 Wu et al.12 confirmed the previous findings by reporting that axial flow impellers are more energy intensive than radial flow impellers under unbaffled conditions. They also demonstrated that the impeller power consumption to achieve off-bottom solids suspension decrease with the removal of baffles. Additionally, they found that a power saving of ≈70% could be achieved under unbaffled conditions even with relatively very high solids concentration (>0.40 (v/v)). All of the above studies involve solid-liquid systems with single impellers. There is still a lack of understanding on the influence of solids concentration on specific impeller power consumption especially when it is expressed in the form PJS/MS for solid-liquid systems with multiple impellers, despite the widespread use of this



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configuration in the industry especially in mineral processing. Therefore, it would be interesting to study specific impeller power (PJS/MS) characteristics in taller vessels fitted with dual impellers as a function of solids concentration. In many cases, such as in multiphase catalytic reactions and crystallization, off-bottom solids suspension alone is not sufficient and a greater degree of particle dispersion is required to enhance process efficiency.26, 27 There have been many studies in the literature on impeller power consumption required to achieve complete particle dispersion. Hicks et al.26 showed that, while at NJS, solids dispersion level decreases with increasing solids concentration up to a value of 0.40 wt% and increases after that. Recently, Wang et al.28 proposed a simple model to estimate the impeller power consumption to achieve a homogenous solids suspension for different volumetric solids concentrations (CV). They showed that axial flow impellers are the most efficient at dispersing solids up to CV = 0.2 (v/v). Wu et al.24 observed that a lower specific impeller power input is required for particle dispersion at a very high solids concentration (CV = 0.4 (v/v)) under unbaffled conditions when compared to that under baffled conditions. There have been many studies in the literature to quantify and enhance solid-liquid mass transfer in agitated vessels, but the majority of them involve low solids concentration.29-31 Harriott32 showed that the mass transfer coefficient was not affected by the solids concentration up to 0.053 (v/v). Similar observations were made by Lal et al.33 for CV up to 0.1 (v/v). Cline34 suggested that the mass transfer coefficient decreases with increasing solids concentration at a constant impeller speed in the CV range of 0.05 to 0.40 (v/v). Harriott32 reported a correlation to predict the solid-liquid mass transfer coefficient (kSL) applicable to solids concentration up to 0.3 (v/v). He predicted that kSL would increase with increasing solids concentration but did not validate his predictions with experimental data. Bong et al.22 reported that optimum kSL and PJS/MS occurred at a solids concentration of 0.2 (v/v) for a vessel operating at NJS. However, all the above studies involve solid-liquid systems with a single impeller. Similar information on the effect of solids concentration and tank geometry on kSL for multiple impeller systems, especially for dual impeller systems, is lacking. 6 ACS Paragon Plus Environment

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This paper aims to investigate the solids suspension characteristics in a solid-liquid agitated system equipped with two impellers. It is aimed to determine the applicability of Zwietering’s correlation for predicting NJS to the dual impeller agitated system under baffled and unbaffled conditions at high solids concentrations. It is also aimed to investigate the effect of solids concentration, baffling condition, and impeller type on kSL and PJS/MS in a dual impeller agitated vessel. This paper compares the results obtained with dual impellers to those obtained with a single impeller to determine the advantages of using one over the other for the purpose of achieving process intensification.

2. Experimental A schematic diagram of the experimental set-up is shown in Figure 1. Experiments were carried out in a cylindrical, flat-bottomed Perspex tank with a diameter (T) of 0.2 m inside an outer cubical Perspex tank. The liquid height H was set to 1.5 T for vessels agitated with dual impellers. The baffled tank was fitted with four equally spaced baffles with the width (B) equal to T/12. The annulus between the outer and inner tanks was filled with water to minimize optical distortion during flow visualization.



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Figure 1 - Schematic diagram of equipment setup for dual impeller system, H = 1.5T, C = T/4, D = T/3, B = T/12, S = D The impellers used in this work are shown in Figure 2. Two impeller combinations namely, two 6-bladed Rushton turbines (RTRT) and an A310 hydrofoil plus a 6 bladed-45°pitched blade turbine, both downward pumping, (A310PBT) were used. A310PBT rather than A310A310 was chosen as the impeller configuration for generating axial/mixed flow in this work because A310 as the bottom impeller can ensure efficient off-bottom suspension while the downward pumping PBT as the top impeller can generate mixed-axial flow and relatively higher levels of turbulence in the vessel. This combination, therefore, will not only enhance the solids dispersion in the vessel but also enhance the solid-liquid mass transfer, which is also an important objective of this work. The impeller diameter (D) was equal to T/3 except for A310, which was 0.064 m (T/3.125) in diameter. The off-bottom clearance (C) was set equal to T/4 for all experiments. The impeller spacing (S) between the impellers in the dual impeller experiments was equal to the impeller diameter (D).

Figure 2 - Impeller types used in the study: (a) Rushton turbine, (b) Pitched blade turbine (downward pumping), (c) A310 hydrofoil (downward pumping) For all experiments, NaOH solution (ρL = 1000 kg/m3) with the concentration of 0.025M was used as the liquid phase and cation exchange resin particles were used as the solid phase. To prepare NaOH solution, analytical grade NaOH pellets were dissolved in deionised water. The ion exchange resin particles (Dowex Marathon C (H)) supplied by IMCD, Australia had an average diameter (dp) of 0.6 - 0.7 mm and density (ρs) of 1220 kg/m3. The resin particles were washed with deionised water to remove any contaminants and dried using suction-filtration before use. The solids concentration (CV) was varied from 8 ACS Paragon Plus Environment

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0.05 to 0.35 (v/v) to study its effect on impeller power consumption and solid-liquid mass transfer coefficient. All experiments were conducted at the critical impeller speed required to ‘just suspend’ all particles off the tank bottom (NJS). A method proposed by Hicks et al.26 was used to determine NJS. The impeller speed was initially increased to above NJS so that no particle remained motionless at the vessel bottom (Figure 3a). The impeller speed was then decreased until a thin layer of solid bed appeared at the vessel bottom whose height is designated as HB (Figure 3c). The impeller speed was then increased slightly until the solid bed just disappears or HB = 0 and this impeller speed was designated as NJS (Figure 3b). This method was demonstrated by Wu et al.12 and Wang et al.13 to be quite reliable even at higher solids concentrations.

Figure 3 - States of solids suspension and distribution in a dual impeller agitated system: (a) N > NJS, homogeneous suspension, H = HS, (b) N = NJS, HB = 0, (c) N < NJS, HB > 0 A typical axial solids concentration profile at NJS is reported by Hicks et al.26 and Wang et al.28 Essentially, there is a clear demarcation between the lower region with higher solids concentration and the upper region where the solids concentration is around zero. The height of the lower region is often referred to as the cloud height, HS (Figures 3b and 3c). In this work, cloud height was determined visually 9 ACS Paragon Plus Environment


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at NJS and other impeller speeds. It was found that the slurry was not necessarily homogenous when the cloud height reached the liquid surface (HS = H). The minimum impeller speed required to ‘just completely disperse’ the solids such that HS = H was denoted as NJCD. The impeller power consumption was determined by measuring the torque experienced by the impeller using a torque transducer (Burster 8645-500) and was calculated using the following equation: = 2

(2)

where power, P (W) is a function of impeller speed, N (rps) and torque,

(N.m). The impeller power

consumptions at NJS and at NJCD were denoted as PJS and PJCD, respectively. The specific power consumption based on the mass of suspended solids at ‘just suspended ‘conditions (εJS) was calculated using Eq. (3): ! =

"#$ %$

(3)

where εJS (W/kg) denotes the specific impeller power consumption and MS (kg) is the total solids suspended in the vessel. The mass transfer experiments were conducted by measuring the changes in NaOH concentration due to the interphase exchange of cations. The change in sodium concentration was determined by measuring the solution conductivity using an electrical conductivity meter (HACH, sensionTM HQ40d). The conductivity probe was placed adjacent to the shaft at mid-liquid height position. The volumetric solid-liquid mass transfer coefficient, kSLap (s-1), which is the product of the solid-liquid mass transfer coefficient, kSL (m/s) and the solid-liquid interfacial area per unit volume of solid, aP (m-1) was determined by measuring the change in NaOH concentration and using it in Eq. (4):35, 36 &' ()* +,- / = −12 3 4 )*

-

+, .

(4)


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where [CNa] and [CNa]0 (mol/m3) are the sodium molar concentration at any given time, t and t=0, respectively. A linear plot of the left-hand side of the equation (4) against time ‘t’ will yield kSLap as the slope of the straight line. The solid-liquid interfacial area, aP was calculated using the following equation: 3 = 7

5*6 89

(5)

where Cv (v/v) is the volumetric solids concentration and d32 (m) is the Sauter-mean particle diameter which was determined to be 6.24 x 10-4 m for ion exchange resins using Malvern particle size analyzer. The solid-liquid mass transfer coefficient kSL can then be determined by dividing kSLap by ap.

3. Results and discussion 3.1. NJS results and their estimation using Zwietering’s correlation The section discusses the applicability of Zwietering’s correlation (Equation 1) in solid-liquid systems operating at high solids concentration in agitated vessels.

The NJS data for RTRT and A310PBT

impellers are shown in Figures 4a and 4b as a function of CV for both baffled and unbaffled conditions. Under both baffled and unbaffled conditions, NJS increases with increasing CV for both impeller arrangements. No significant difference was found in NJS values between those for baffled and unbaffled tanks for systems using both RTRT and A310PBT impellers. Close examination of Figures 4a and 4b also shows that NJS values for RTRT are lower than those for A310PBT impellers. The NJS values estimated using Zwietering’s correlation (shown as continuous lines) are compared with experimental results in Figures 4a and 4b. The S values used in the estimations, which were obtained using back-solving analysis, are shown in Table 1. The estimated NJS values are slightly higher than the experimental values at low CV (< 0.2 (v/v)) and lower at higher CV for both impeller combinations. It is especially the case for A310PBT under unbaffled condition (Figure 4b). Although Zwietering2



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investigated solids concentration only up to CV ≈ 0.12 (v/v), the results of this study suggest that Zwietering’s correlation is applicable up to 0.35 (v/v) under both baffled and unbaffled conditions for dual impeller systems.

Figure 4 – Experimental NJS values compared with those predicted using Zwietering correlation: (a) baffled vessel, (b) unbaffled vessel

Table 1 – Values of Zwietering constants, S determined from experimental results RTRT

A310PBT

Baffled Unbaffled Baffled Unbaffled Zwietering

5.8

5.5

10.5

10.5

constant, S

3.2. Impeller power consumption at NJS The specific impeller power input values at NJS based on slurry volume (PJS/V) are shown in Figure 5 for RTRT and A310PBT under baffled and unbaffled conditions for a CV range of 0.05 – 0.35 (v/v). It can be seen that (PJS/V) increases with increasing CV in both baffled and unbaffled vessels. The increase in (PJS/V) with an increase in CV can be attributed to increased particle-particle, particle-liquid, and particle12 ACS Paragon Plus Environment

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equipment collisions as suggested by Bubbico et al.37 and also to increased slurry viscosity. Values for effective slurry viscosity predicted using different correlations are discussed further and reported elsewhere.38 The increase in (PJS/V) with increasing effective slurry viscosity is consistent with results presented by other authors.39, 40 It is also clear from Figure 5 that the removal of baffles leads to significant energy savings in dual impeller systems. Similar reductions in energy consumption due to the removal of baffles were reported by Wang et al.19 for A310 and PBT in a single impeller system. Interestingly, (PJS/V) values for RTRT (radial pumping impellers) are lower than those for A310PBT (axial/mixed downward pumping impellers) under both baffled and unbaffled conditions. These results suggest that it is beneficial to use RTRT over A310PBT to achieve ‘just suspended’ conditions. Another way impeller power consumption at NJS can be expressed is on the basis of total slurry mass (PJS/(MS+ML)), where MS and ML are total mass solids and liquid, respectively. The trends in (PJS/(MS+ML)) curves (data not shown) are similar to those for (PJS/V) curves as shown in Figure 5. The main reason for this is the nearly constant (MS+ML) values (= 8.44 to 8.95 kg) for a CV range of 0.05 – 0.35 (v/v) due to nearly similar densities of the solid and liquid phases (ρS = 1220 kg/m3 and ρL = 1000 kg/m3) used in our experiments.



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Figure 5 – Impeller power input at NJS per unit slurry volume (PJS/V) as a function of CV: (a) baffled vessel (b) unbaffled vessel

Figure 6 – εJS (= PJS/MS) as a function of solids concentration for the two dual impeller configurations: (a) baffled vessel, (b) unbaffled vessel The εJS (= PJS/MS) values for the dual impeller system are shown in Figures 6a and 6b for baffled and unbaffled conditions, respectively. The εJS values for both RTRT and A310PBT combinations decrease with increasing CV, reach a minimum at a CV value of about 0.2 (v/v), and increases thereafter under baffled condition (Figure 6a). Similar trends are observed for both impeller combinations under unbaffled condition, but the increase in εJS beyond Cv = 0.2 (v/v) is not large. This trend is consistent with the 14 ACS Paragon Plus Environment

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results reported by Wang et al.,13 who studied the effect of high solids concentration on εJS using glass particles. Similar results were also reported by Bong et al.22 who found the minimum εJS value around 0.20-0.25 (v/v) in a single impeller system using ion exchange particles as the solid phase. They defined CV at which the εJS value was minimum as the “optimum solids concentration (CVop)”. For CV(op), more solids are suspended per unit impeller power (kg/W) than at any other solids concentration. For Cv lower than CV(op), the power input by the impeller is not fully utilised for solids suspension because a large proportion of it is used unnecessarily to move the liquid around. For Cv greater than CV(op), additional power input to suspend the additional amount solids in disproportionally high leading to poor impeller energy efficiency. The results obtained in this work indicate that operating a solid-liquid mixing vessel with dual impellers at a CV of 0.20 (v/v) would result in more efficient impeller power usage. Similar findings were observed by Wang et al.19 who used denser particles (ρS = 2500 kg/m3) using a dual A310 configuration under baffled conditions. The impeller power consumed in vessels with multiple impellers largely depends on the impeller type and geometry, number of impellers, and impeller spacing. Figure 6 shows that unbaffled tanks require significantly lower power for solids suspension for both RTRT and A310PBT impeller configurations. The reduction in εJS due to the removal of baffles is 70-75% for RTRT and 50-60% for A310PBT impellers. Similar reductions in εJS due to the removal of baffles were reported by Wu et al.24 for dual radial and dual axial pumping impellers at CV = 0.4 (v/v). They noted that the reduction in εJS for dual radial pumping impellers is greater than that for dual axial pumping impellers. The flow phenomena that could be attributed to the specific power reduction for both RTRT and A310PBT is an inward-spiralling liquid flow that is dominant under unbaffled conditions which moves the particles away from the tank walls towards the center and suspending them below the impeller. Similar reasoning was made by Assirelli et al.41 who suggested that the unchaotic liquid swirling motion formed in unbaffled tanks leads to a reduction in the impeller power consumption compared to that in baffled tanks.



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RTRT combination consumes less power at NJS compared to A310PBT under both baffled and unbaffled conditions (Figure 6). The difference in εJS values between these two impeller combinations is around 4050% and 60-70% for baffled and unbaffled vessels, respectively. Similar findings were made by Wu et al.24 who reported that εJS values for low power number dual axial pumping impellers are higher than those for high power number dual axial pumping impellers at a solids concentration of 0.4 (v/v) under both baffled and unbaffled conditions. The above results can be attributed to the homogenous distribution of particles observed in our experiments for RTRT. In general, the bottom impeller in a dual impeller system is largely responsible for solids suspension at the tank bottom while the top impeller is responsible for particle distribution in the upper volume of the vessel. In the case of RTRT, the turbulent flow produced by top RT impeller complimented that produced by the bottom RT impeller. The combined flow fields generated by upper and lower RT impellers led to fewer solids dropping out of suspension thereby leading to a lower NJS value and consequently lower impeller power consumption.42

3.3. Particle dispersion at NJS At NJS, all particles are suspended off the tank bottom, and a major fraction of them are lifted to higher levels in the liquid. The maximum height to which the particles are lifted is called the ‘cloud height, HS’. Cloud height is the result of interaction between the flow patterns generated by the impeller, which depends on the baffle arrangement, and the particle settling velocity, which has a distribution depending on the particle size distribution.42 Cloud height values at NJS normalized with liquid height (HS/H) are shown for dual impeller systems in Figures 7a and 7b for baffled and unbaffled vessels, respectively as a function of CV. The liquid level was set equal to 1.5T in all dual impeller experiments. The cloud height increases with increasing CV until HS is equal to H. The cloud height becomes equal to the liquid level at CV = 0.15 (v/v) for the baffled tank and CV = 0.1 (v/v) for the unbaffled tank. These results are further substantiated in Figure 8 which shows NJCD (the impeller speed at which HS = H) values are either equal or slightly greater than NJS values at lower CV indicating that the cloud height would be lower than or


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equal to H at NJS. At higher CV, NJS values are greater than NJCD values indicating that complete particle dispersion is attained under these conditions at NJS. Figures 7a and 7b show that cloud height values for RTRT at Njs in the unbaffled vessel are essentially the same as those observed in the baffled vessel. But, cloud height values for A310PBT in the baffled vessel are lower than those in the unbaffled vessel at low CV ( 0.2 (v/v), the cloud height for A310PBT becomes equal to the liquid height in both baffled and unbaffled vessels. These results also show that the effect of impeller type on the cloud height in dual impeller systems is marginal. At low CV, RTRT at NJS under baffled condition outperformed A310PBT slightly in achieving ‘just complete dispersion’ condition while the effect is opposite under unbaffled condition. At higher CV, there is no difference in cloud height between the impeller types (Figures 7a and 7b).

Figure 7 - Normailized cloud height (HS/H) while operating at NJS as a function of CV: (a) baffled vessel, (b) unbaffled vessel



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Figure 8 - NJS and NJCD values as a function of CV: (a) baffled vessel, RTRT impeller, (b) unbaffled vessel, RTRT impeller, (c) baffled vessel, A310PBT, (d) unbaffled vessel, A310PBT

3.4. Impeller power consumption to attain ‘just completely dispersed’ condition The impeller power consumption to achieve ‘just complete dispersion’, (PJCD), in dual impeller systems, are shown in Figures 9a and 9b for baffled and unbaffled vessels, respectively. The PJCD value increases with increasing CV for both RTRT and A310PBT impeller configurations under baffled conditions (Figure 9a). However, under unbaffled conditions, PJCD increases slightly with increasing CV, reaches a maximum at CV = 0.2 (v/v) and decreases slightly thereafter (Figure 9b). These results can be explained using NJCD results shown in Figure 8. As PJCD is directly proportional to NJCD, an increase in NJCD would lead to an increase in PJCD and vice versa. 18 ACS Paragon Plus Environment

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A comparison of Figure 9a with 9b shows that there is a substantial decrease in PJCD due to the removal of baffles at any given CV for both impeller configurations used. However, the extent of the energy savings is the highest at higher CV (CV >0.2 (v/v)). These results are substantiated by other studies in the literature which showed that unbaffled tanks lead to lowering of specific impeller power consumption for solids suspension.25, 28, 43 Figure 9 also shows RTRT has lower PJCD values compared to A310PBT under both baffled and unbaffled conditions. The decrease in PJCD for RTRT compared to A310PBT is significant (50 - 58%) under baffled conditions while it is about 40% under unbaffled conditions. These results suggest that dual radial flow impellers are more efficient at achieving ‘just complete dispersion’ conditions than axial/mixed flow impellers. The impeller power consumption to attain varying levels of cloud heights was also measured to investigate its impact on cloud height at different solids dispersion levels, and the results are shown in Figure 10 for dual-impeller systems. For all experiments, CV was maintained at 0.2 (v/v) and power measurements were obtained at HS = 0.5H, 0.7H, 0.9H, and H, and also for N >NJCD. Cloud height values shown indicate that RTRT requires lower power to attain varying levels of cloud height than A310PBT. Also, unbaffled systems require lower power to achieve a certain degree of solids distribution. Cloud height is more sensitive to changes in power input for RTRT under unbaffled condition. This is shown as a rapid increase in HS/H when impeller power input is increased. Similar findings were reported by Wang et al.28 but for baffled tanks. They found that the decrease in cloud height with a decrease in the impeller speed from 500 to 300 rpm is significant (10 – 20%) for baffled tanks compared to that in unbaffled vessels.



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Figure 9 - PJCD values as a function of CV: (a) baffled vessel, (b) unbaffled vessel

Figure 10 – Dispersion of solid particles at constant particle loading (CV = 0.2 (v/v))

3.5. Solid-liquid mass transfer coefficient kSL The solid-liquid mass transfer coefficient (kSL) values obtained using RTRT and A310PBT in baffled and unbaffled vessels for a range of CV are shown in Figure 11. It can be seen that kSL increases with increasing CV, reaches a maximum and decreases thereafter. The CV with the highest kSL value is defined as CV(max) and it occurs at a CV value of 0.2 (v/v) for both dual impeller systems studied. Similar findings 20 ACS Paragon Plus Environment

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were reported by Bong et al.22 who showed that the kSL value in a single impeller system operating at NJS increased with increasing CV up to a maximum at CV = 0.20 (v/v) and decreased thereafter. They attributed the increase in kSL with increasing CV to increasing NJS values and associated increased turbulence intensity levels. Turbulence intensity in the continuous phase influences the advective as well as the diffusional mass transfer at the solid-liquid interface. Therefore, an increase in turbulence intensity around the particle would lead to an increase in the mass transfer rate and thus the mass transfer coefficient. The decrease in kSL for CV > 0.20 (v/v) was attributed by Bong et al.22 to turbulence dampening due to increasing effective viscosity of slurry (ηslurry) and its effect on diffusional mass transfer. Also, particle-particle interactions become more frequent with increasing ηslurry, which decreases the solid-liquid interfacial area thereby decreasing the mass transfer rate.44,

45

It is expected that the

changes in turbulence intensities and consequent changes in the trends of kSL versus CV plots for denser particles will be similar to those found in this work but they should be verified by carrying out further experimental work. It is also clear from Figures 11a and 11b, at any given CV, baffles have minimal effect on kSL especially for RTRT. There is a slight increase in kSL with the removal of baffles for A310PBT. These results are consistent with those reported by Bong et al.46 for a single impeller system who reported that kSL values for RT at NJS are similar under both baffled and unbaffled conditions for a CV range of 0.08 – 0.3 (v/v). Harriott32 also found that kSL values in both baffled and unbaffled single impeller tanks were similar at low solids concentration. However, Nienow et al.47 reported that, for single impeller systems, surface aeration occurred in unbaffled tanks at high impeller speeds due to vortex formation resulting in lower gas-liquid mass transfer coefficient values compared to those in baffled tanks. Surface aeration could occur also in baffled solid-liquid agitated tanks at relatively higher impeller speeds thereby leading to turbulence dampening and consequent decrease in kSL. However, the entrainment of air bubbles was not observed at NJS in this work under both baffled and unbaffled conditions probably because the liquid flow patterns and turbulence intensity produced by dual impellers in solid-liquid system are different from



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those produced in single impeller systems. Therefore, the influence of surface aeration on kSL was not explored in this study. It can also be seen from Figure 11a that, under baffled conditions, the kSL values obtained for both RTRT and A310PBT are nearly the same at any given CV. The results also show that under unbaffled conditions, the kSL values for A310PBT are higher than those for RTRT for a CV range of 0.05 - 0.35 (v/v). As mentioned earlier, it was observed during experiments that particle distribution was more homogenous in the case of RTRT suggesting that the liquid flow produced by each RT impeller complimented each other and aided in particle suspension and dispersion. On the other hand, the flow generated by A310PBT under unbaffled conditions may have interfered with each other leading to an increase in levels of chaotic mixing and therefore increased mass transfer.18 Pangarkar et al.30 also suggested that different impellers produce different levels of turbulence and therefore have different levels of influence on solid-liquid mass transfer.

Figure 11 – Solid-liquid mass transfer coefficient as a function of CV: (a) baffled vessel, (b) unbaffled vessel

3.6. Optimum solids concentration The specific impeller power consumption for solids suspension for a range of solids concentrations under different impeller and vessel configurations was discussed above. It was shown in dual systems that εJS 22 ACS Paragon Plus Environment

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can be minimized by operating the solid-liquid mixing system at a higher solids concentration called CV(op) which is higher than CV values hitherto used. It has been suggested by Wang et al.19 that the value of CV(op) is dependent on the slurry flow pattern within the tank. Changes in the flow pattern can be estimated from the impeller Reynolds number, which can be expressed as :;?@@A B#$ C 9 D>?@@A

(6)

where ρslurry is the slurry density (kg/m3) which is calculated using EFGHIIJ = EF KL + E2 1 − KL , NJS is

the minimum impeller speed to achieve ‘just suspended’ condition (rps), D is the impeller diameter (m),

and ηslurry is the slurry viscosity (Pa.s) which can be estimated using Fedors’ correlation and is as follows:48

.*P / R *P

OFGHIIJ = OI (1 + Q

(7)

where nr is the viscosity of the carrier fluid (Pa.s), φm is the maximum volume fraction to which the particles can pack. Fedors used φm = 0.63 for a system containing permanent aggregates in a Newtonian liquid. However, in later studies, φm was reported to be equal to 0.68 which gave good agreement between experimental data and model predictions.38 Therefore, φm = 0.68 was used in this work. The impact of solids concentration on ReImp for dual impeller configurations in baffled and unbaffled vessels is shown in Figure 12. It can be seen that ReImp decreases with increasing CV regardless of baffling condition or impeller configuration. Figure 12 also shows that ReImp remains above 10000 at CV = 0.35 (v/v) for A310PBT regardless of baffle arrangement, whereas ReImp for RTRT falls just below 10000. These results indicate that up to a CV value of 0.35 (v/v), the flow regime in the tank is turbulent and solids suspension can still be achieved without excessive power draw. By operating at higher CV (> 0.2 (v/v)), the mixing vessel can achieve a higher throughput or the required vessel size to achieve the same



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throughput is smaller which will lead to an increase in process efficiency and decrease in capital costs, which meets the one of the criteria of process intensification. Wang et al.13 examined various ways of optimizing solid-liquid systems by considering impeller and tank geometry. They showed that the removal of baffles led to significant increases in energy efficiency. Similar observations are found in this study for dual impeller systems. Though the removal of baffles has been shown to increase mixing time, this is not an issue in mineral processing operations because the time scales for reactions or mass transfer are still an order of magnitude greater than the mixing time.12 In addition to the removal of baffles, further energy savings can be achieved by optimizing impeller design such as using radial flow impellers as discussed earlier. The benefits of operating a solid-liquid system at higher CV are not only restricted to significant energy savings, but it also leads to increased levels of mass transfer as shown above. Mass transfer is intensified with an increase in CV due to the associated increase in NJS, which in turn will lead to increases in (PJS/V) and turbulence levels in the mixing vessel. As a consequence, the kSL values increases at higher CV values. Also, with increasing CV, the impeller energy efficiency increases as the amount of energy required to achieve off-bottom solids suspension per mass of solids (W/kg) decreases. Table 2 summarizes the CV(op) values and corresponding εJS values. It also includes CV(max) and corresponding kSL values for both impeller configurations and baffling conditions.


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Figure 12 – Effects of CV on impeller Reynolds number (Reimp) operating at NJS using viscosity (ηslurry ) values estimated using the correlation proposed by Fedors48

Table 2 - CV(op) and CV(max) values with corresponding εJS and kSL values, respectively

Impeller

Liquid

Baffle

CV at which εJS

Corresponding

CV at which

Corresponding

height

arrangement

is the lowest,

εJS (W/kg)

kSL is the

kSL (mm/s)

(CV(op)) (v/v)

highest, (CV(max)) (v/v)

RTRT

H = 1.5 D

Baffled

0.15-0.20

2.31-2.33

0.20

0.11

RTRT

H = 1.5 D

Unbaffled

0.20

0.63

0.20

0.11

A310PBT

H = 1.5 D

Baffled

0.15-0.25

4.33-4.42

0.20

0.12

A310PBT

H = 1.5 D

Unbaffled

0.20

1.85

0.20

0.13



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3.7. Case study To illustrate the benefits of adopting some of the recommendations highlighted in earlier sections of this work, a case study is presented for the parameters shown in Table 3. A hypothetical benchmark design, which was considered as the ‘standard’ design for solid-liquid systems by Wang et al.,19 is used as the existing design in this case study. Wang et al.19 suggested that solid-liquid mixing tanks in the minerals industry operated at relatively low solids concentrations under fully baffled conditions. Based on this, the CV value chosen for the existing design is 0.1 (v/v), and a single A310 impeller is chosen as the impeller for the existing design. The new solid-liquid agitated vessel design, one with a single impeller and one with a dual impeller configuration are also shown in Table 3 to highlight the difference between the two. The single impeller results were obtained in this work by conducting experiments using the 0.2 m diameter tank with a slurry height of 0.2 m while the dual impeller results were obtained using the 0.2 m diameter tank but with a slurry height of 0.3 m. Both single and dual impeller mixing vessels include radial pumping impellers under unbaffled conditions. The vessels were operated at higher solids concentrations (CV = 0.2 (v/v)), which is significantly higher than that of the standard design. The impeller speed to ‘just suspend’ and ‘just completely disperse’ solids for the new designs are found to be lower than those in the standard design resulting in significant savings in power usage. It should also be noted that the degree of solids dispersion (cloud height) and the kSL value increase in the new designs. For both single and dual impeller systems, the values of each parameter are very similar except for εJS and PJCD values. Though the power consumption in the dual impeller system to achieve ‘just complete dispersion’ conditions is greater, the lower value of εJS implies better energy utilization for solids suspension. These results suggest that a dual impeller agitated vessel operating under the unbaffled condition is preferable to be used with higher Cv because it improves power efficiency (lower εJS) and achieves kSL values that are similar to those in single impeller systems.


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Table 3 – Vessel/impeller dimensions and design parameters for an existing and new solid-liquid mixing vessels. Design parameters values for the new design (NJS, NJCD, Cloud height at NJS, εJS, PJCD, kSL) were determined in this study from experimental work. Specifications

Standard design

New design

New design

(single impeller)

(dual impellers)

Tank diameter (T)

0.2 m

0.2 m

0.2 m

Liquid height (H)

H=T

H=T

H = 1.5T

Baffles

4

0

0

Impeller

A310

RT

RTRT

Impeller diameter (D)

T/3.125

T/3

T/3

Solids concentration (CV)

0.1 (v/v)

0.2 (v/v)

0.2 (v/v)

Agitator speed for just off-bottom

730 rpm

400 rpm

430 rpm

760 rpm

400 rpm

390 rpm

Cloud height (HS/H) at NJS

0.84

0.97

1.0

Specific impeller power

3.94 ±0.02% W/kg

0.88 ±0.02% W/kg

0.63 ±0.02% W/kg

Power consumption at NJCD (PJCD)

2.98 ±0.02% W

1.16 ±0.02% W

1.44 ±0.02% W

Solid-liquid mass transfer

0.097 mm/s

0.11 mm/s

0.11 mm/s

solids suspension (NJS) Agitator speed for complete solids dispersion (Hs = H), (NJCD)

consumption at NJS (εJS)

coefficient (kSL)



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3.8. Mathematical Correlations 3.8.1. Correlation for estimating the specific impeller power consumption, εJS Recently, Bong et al.22 have shown that the impeller power consumption at NJS in a single impeller agitated vessel can be determined using the following equation: = EFGHIIJ

(8)

where NP is the single impeller power number, ρslurry is the density of the slurry (kg/m3) and D is the impeller diameter (m). To account for the influence of particles on impeller hydrodynamics and therefore impeller power consumption, Bong et al.22 incorporated the parameter k into Eq. (9) and by combining Eq. (3) and Eq. (8), the following is obtained: S = = % "

$

8 V T BU >?@@A B#$ C

%$

(9)

The parameter k is a function of vessel and impeller geometries and is shown in Table 4 for the mixing systems studied in this work. These values were obtained using experimental data for the impeller power and speed, and performing a back-solving analysis. The critical impeller speed NJS can be estimated using the Zwietering correlation (equation 1). The X term

in Eq. (1) can be expressed as a function of CV by the equation = ($ / ( * P /. Though the exponent

*

P

for X varies, it is equal to 0.13 according to Zwietering.2 The same value of 0.13 is assumed applicable for solids concentration of 0.05 to 0.35 (v/v) and is used in this work. Even though Eq. (1) was derived using solid-liquid mixing vessels fitted with a single impeller. Dutta and Pangarkar18 showed that the

empirical correlation for NJS for single impeller systems could also be applied to agitated reactors fitted with multiple impellers.


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By substituting Eq. (1) into Eq. (9), the following equation for the specific impeller power consumption is obtained for the case of the dual impeller system: ! = 1 W

BU XY >?@@A %$

CV

Z[

\..] 7^

..9

..bV

_ / a

C ..hV

..]8

d ]..e6 cW Z( /g d

]fe6

i

(10)

where εJS is the specific impeller power consumption (W/kg), k is a constant, NP(DI) is the cumulative impeller power number for dual impellers which can be found in Table 4, ρslurry is the slurry density (kg/m3), D is the impeller diameter (m), MS is the mass solids (kg), S is the Zwietering constant, ν is the kinematic viscosity of the slurry (m2/s), dp is the particle diameter (m), g is the gravitational acceleration constant (m/s2), ρS and ρL are the densities of the solid and liquid phases, respectively (kg/m3) and CV is the volumetric solids concentration (v/v). Figure 13 is a comparison of experimental data obtained in this study and values obtained using Eq. (10). It can be seen that the values estimated by Eq. (10) were in good agreement with experimental data for dual impeller systems for a CV range of 0.05 – 0.35 (v/v) with the vast majority of data points situated within a ±15% band.

Figure 13 – Comparison of εJS experimental data with values predicted using Eq. (10)



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3.8.2. Correlation to estimate the solid-liquid mass transfer coefficient There are many correlations reported in the literature for estimating the solid-liquid mass transfer coefficient in agitated vessels over a wide range of Reynolds numbers. Most of these mathematical correlations are in the form of the following equation.22, 35, 49 ℎ =

T$ 7U Ck

= 2 + l:; . m .

(11)

where Sh is the Sherwood number, dp is the particle diameter (m), DA is molecular diffusivity (m2/s), Re is the Reynolds number, Sc is the Schmidt number, and A is a constant. A is determined using a regression analysis of the experimental data. The contribution of asymptotic molecular diffusion from a fixed sphere based on film theory is taken into account in Eq. (11) by using the constant 2.50 This value is widely used in mathematical correlations for mass transfer in agitated slurries involving spherical particles. Based on the boundary layer theory, the exponent of the Schmidt number is chosen as 0.33, though it varies from 0 - 0.5 depending on hydrodynamic conditions.32,

35

Many investigators using a wide range of solids concentrations have

agreed that the exponent for the Reynolds number should be equal to 0.5 for solid-liquid mixing systems and therefore it is chosen for this work.32, 34, 35 The particle Reynolds number used in Eq. (11) is based on Kolmogoroff theory of isotropic turbulence and is defined by Eq. (12):51 :; = (

b n 7U

o8

/

/

(12)

where ε = energy dissipation rate per unit mass of liquid (W/kg), dp is the particle diameter (m), and ν is the kinematic viscosity of the liquid (m2/s). The energy dissipation rate per unit mass liquid, ε, is defined as follows:


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S = %

"

(13)

where P is the total impeller power consumption (W), and ML is the total mass liquid in the tank (kg). By substituting Eq. (1), Eq. (8), Eq. (13) and incorporating the k parameter into Eq. (12), the following equation for the modified particle Reynolds number (Rep) is obtained as a function of CV: :; = p

..bV ..]8 8 +U XY d>?@@A XV ..] cu_d fd ag ..9 C f..hV cW d Z(]..e6 /g b 7U v 7U sto r d d ]fe6

T q

o8

/

w

(14)

Eq. (14) can be used to determine Rep in the absence of experimental impeller power consumption data as it’s a function of solids volume fraction CV. The mass transfer correlation (equation 11) can now be rewritten as: ℎ = 2 + l:;. m .

(15)

The value of A is obtained by rearranging Eq. (15) and is as follows: x y ..88

= l :;.

(16)

By plotting (y ..88 versus Rep0.5 in an x-y graph, the value of A can be determined and is shown in Figure x

14. It can be seen that the plots for all the mixing systems studied are not linear where (y ..88 increases x

with increasing Rep0.5, reaches a maximum and decreases thereafter. This trend is similar to the experimental results for kSL with increasing CV. This is expected as Sh is a function of kSL (equation 11) and Rep0.5 accounts for changes in CV (equation 14).



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Figure 14 - (Sh-2)/Sc0.33 versus ReP0.5 for CV = 0.05 - 0.35 (v/v), continuous lines represent equation: z{| z}~.

~. = −_~. a + _ a − } |

A mathematical equation that represents the parabolic trend of the data points was determined by carrying out a non-linear regression analysis. The parabolic nature of the data trend indicates that it could be simulated mathematically using a quadratic equation as follows: x y ..88

= −3_:;. a + _:;. a − m

(17)

From Eq. (16) and rewriting Eq. (17), we get l = −3_:;. a + − m_:;. a

(18)

The constants a, b and c that were determined by performing a regression analysis are shown in Table 4 for the mixing systems studied. The mean absolute % error is commonly used as a measure of the difference between predicted and observed values.52 The mean absolute % error values that were determined using equation (19) for each set of experiments are shown in Table 4: ;3' 3&4; % ; = B ∑

_T$ ,> T$ U a T$ U

100%

(19)


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where N is the number of data points, kSL(cal) is the solid-liquid mass transfer coefficient estimated using Eq. (20) and kSL(exp) is the experimental solid-liquid mass transfer coefficient value. Table 4 - Parameters in Eq. (1), (10), (14), (19) and (20) RTRT

A310PBT

Baffled

Unbaffled

Baffled

Unbaffled

S

5.8

5.5

10.5

10.5

k

1.1

1.1

1.1

1.1

NP(DI)

6.5

2.3

2.3

1

a

0.81

2.55

1.46

1.85

b

7.0

17.6

14.1

14.9

c

9.38

24.7

27.6

23.0

Average

2.1

5.1

5.9

3.3

error (%)

By substituting Eq. (18) into Eq. (15), the following equation is obtained: ℎ = 2 + −3_:;. a + − m_:;. a:;". m .

(20)

The Sh values obtained from experimental kSL values and those calculated using Eq. (20) are compared in a parity plot as shown in Figure 15. It can be seen that all data points are situated within the ±10% band. Based on these results, we propose that Eq. (20) can be used to estimate kSL values for mixing systems similar to that used in this work for a CV range of 0.05 to 0.35 (v/v). More experimental work needs to be carried out if Eq. (20) is to be used for estimating kSL for CV values outside the range studied in this work as well as mixing systems with a different tank and impeller geometry.



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Figure 15 - Comparison of predicted and experimental values of Sh

3.8.3. Mathematical model to estimate impeller power consumption to ‘just completely disperse’ solids, PJCD A mathematical model to estimate the impeller power consumption required to ‘just completely disperse’ solids throughout the liquid in a solid-liquid system is presented here. In a pure single phase system, the impeller power consumption is defined as = E2

(21)

where P is the impeller power consumption (W), ρL is the liquid density (kg/m3), Np is the single impeller power number, N is the impeller speed (rps) and D is the impeller diameter (m). Assuming a well dispersed two-phase system, the impeller power consumption to ‘just completely disperse’ solids in a solid-liquid system for the dual impeller system can be found by modifying Eq. (8) to the following equation: *C = 1C C

Enhancing Impeller Power Efficiency and SolidâLiquid Mass Transfer

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