Performance of Four Axial Flow Impellers for Agitation of Pulp

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Ind. Eng. Chem. Res. 2010, 49, 4444–4451

Performance of Four Axial Flow Impellers for Agitation of Pulp Suspensions in a Laboratory-Scale Cylindrical Stock Chest Manish R. Bhole* and Chad P. J. Bennington Department of Chemical and Biological Engineering, UniVersity of British Columbia, 2360 East Mall, VancouVer, British Columbia, V6T 1Z3 Canada

Axial flow impellers are commonly used for pulp suspension agitation. Pulp fiber suspensions are non-Newtonian and exhibit a yield stress. In mixing operations, a ‘cavern’ (region of active motion) is created around the impeller, with the size of the cavern affecting the quality of mixing attained. In this work, the cavern size produced by four different axial flow impellers in a Cm ) 3% (mass concentration) hardwood pulp suspension was measured using electrical resistance tomography (ERT) and by analysis of dynamic mixing tests. Cavern size is shown to depend on impeller performance as characterized by power number, NP, and axial force number, Nf. At an equal power consumption of 0.53 kW/m3 the largest cavern was produced by the impeller having the largest values of NP and Nf. The measured cavern volumes compared well with predictions of the axial force model developed by Hui et al. [Hui, L. K.; Bennington, C. P. J.; Dumont, G. A. Cavern formation in pulp suspensions using side-entering axial-flow impellers. Chem. Eng. Sci. 2009, 64, 509], which accounted for interaction between the cavern and the vessel walls. When the cavern just filled the vessel volume, the time constants determined using the dynamic mixing test data reached 90% of their theoretical values (with the estimated standard deviation of (10%), indicating that the chest approached an ideal dynamic response (complete mixing) with the onset of complete motion in the chest. 1. Introduction Mixing operations for pulp and paper manufacture are often accomplished using agitated pulp stock chests. These are rectangular or cylindrical vessels fitted with one or more agitators, usually operated in continuous mode. These chests serve various functions. They act as agitated buffers between sequential processes (providing storage capacity), they blend different chemicals, additives, and pulp furnishes, they are used to modify pulp properties like freeness, and they attenuate highfrequency variation in consistency and other fiber properties before important pulp and papermaking operations. In the latter capacity they complement the action of control loops. A side-entry axial flow impeller having a hydrofoil blade design is most commonly chosen for pulp and paper agitation.2,3 These impellers produce more flow per unit power compared with radial flow impellers and promote macroscale mixing.4 Stock chest design involves selecting the appropriate impeller and power input required to create the desired stock motion in the chest. Due to the non-Newtonian rheology of the pulp suspension this can be a challenge even at low suspension mass concentrations (Cm ) 2-4%), with the suspension yield stress creating a cavern or region of active motion around the impeller. Outside this cavern flow is stagnant in batch operation. EinMozaffari et al.5 characterized macroscale mixing in industrial chests and found that flow nonidealities, including channeling and dead zones, existed and degraded mixer performance. Mixing improved as the size of the cavern increased and when channeling was reduced by locating the stock outlet within the cavern.6 The complete elimination of dead zones requires that the cavern fill the entire suspension volume in the chest, although just achieving this criterion did not produce ideal mixing. As chest mixing performance depends greatly on the shape, volume, and location of the cavern, cavern formation and its dependence on fluid rheology, impeller type, size, and operating speed as * To whom correspondence should be addressed. E-mail: [email protected].

well as its location in the mixing vessel should be characterized and understood. Most investigations of cavern formation have been made using impellers in a top-entry configuration.7-10 In these cases, the cavern was observed to increase in size until it encountered the vessel walls and then increase at a different rate guided by the vessel walls.7 Elson9 studied the effect of impeller geometry by employing a disk turbine, a two bladed paddle, a pitched bladed turbine, and a marine propeller for agitation of 1 wt % Xanthan gum solution. For equal power input, the marine propeller (axial flow impeller) was found to produce the largest cavern, followed by the pitched bladed turbine (mixed flow impeller) and the paddle and disk turbines (radial flow impellers). Serrano-Carreon and Galindo11 also studied cavern development in a top-entry configuration using a 0.25 wt % Carbopol solution. A comparison of relative impeller performance is difficult as each impeller had a different diameter; however, the radial flow impellers (D/T ) 0.5 and 0.57) were found to be slightly superior to the axial flow impeller (D/T ) 0.68). Although this is contrary to other findings, an axial flow impeller behaves increasingly as a radial flow impeller in a nonNewtonian yield bearing fluid. Cavern size can be estimated using models which assume that the force generated by the impeller matches the resistive force of the yield stress at the cavern boundary. On the basis of this force balance, various models for the prediction of cavern size have been developed once the cavern geometry (spherical, cylindrical, or toroidal) was specified.7,10,12 These models assume an unbounded cavern, and hence, their application for side-entry pulp stock chests is limited even at low agitation speeds as cavern-wall interaction is significant. Hui et al.1 developed a model that took the cavern-wall interaction into account. In their work, a side-entry Maxflo impeller was used with the cavern size measured in pulp suspensions of different mass concentrations and fiber types using electrical resistance tomography (ERT). The present work compares the performance (cavern size as a function of operating conditions) of four axial

10.1021/ie901854d  2010 American Chemical Society Published on Web 03/31/2010

Ind. Eng. Chem. Res., Vol. 49, No. 9, 2010

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flow impellers in a Cm ) 3% hardwood pulp suspension. Since all the impellers have the same diameter, their performance can be compared under similar operating conditions (equal power per unit volume and correlated with power number, NP, and axial force number, Nf, for similar operating conditions). Dynamic tests were conducted to measure the fully mixed volume under continuous operating conditions and link mixing behavior with cavern size measured by using ERT in batch operation. 2. Experimental Section A transparent Plexiglas cylindrical stock chest (T ) 38.1 cm) was used to mix a Cm ) 3% mass concentration hardwood bleached kraft pulp (Domtar, Windsor, QC). The chest was equipped with a side-entry agitation assembly consisting of a 2.2 kW motor with a variable frequency drive. Four axial-flow hydrofoil impellers (all having D ) 16.5 cm) were studied: the Maxflo (Chemineer Inc., Dayton, OH), a marine propeller of pitch ratio 1.5 (Missouri Filter & Process Equipment Co., St. Louis, MO), the FF (Focused Flow) impeller (Philadelphia Mixing Solutions, Ltd., Palmyra, PA), and an A-312 (Afromix, Johannesburg, South Africa), as shown in Figure 1. The impeller clearance from the bottom (C) was fixed at 12 cm, and the clearance from the rear wall (offset) was maintained at E ) 7 cm. This configuration gave C/D ) 0.7 and E/D ) 0.4 within the typical range recommended for industrial pulp chests, C/D ) 0.5-1.5 and E/D ) 0.3-1 (AGIMIX International, Uddevalla, Sweden). The stock height was maintained at 30.5 cm, giving Z/T ) 0.8. The net shaft torque, M, was obtained using an in-line inductive rotary torque transducer (Staiger Mohilo, Germany) by subtracting the torque needed to rotate the impeller in air (bearing friction) from that measured in operation. The power number, NP was calculated using NP )

P where P ) 2πNM FN3D5

(1)

Nf was obtained by measuring the axial thrust force, FA, in a top-entry cylindrical mixing vessel using the gravimetric technique described by Bhole et al.13 Nf )

FA FN2D4

Figure 1. Photographs of axial flow impellers (insets show side views): (A) Maxflo, (B) A-312, (C) marine propeller, and (D) FF impeller. All impellers have D ) 16.5 cm.

(2)

Cavern size and shape were measured using a P2000 (ITS, Manchester, U.K.) electrical resistance tomography unit. The laboratory mixing chest was fitted with four equally spaced sensor planes, each consisting of 16 square (2.5 × 2.5 cm2) stainless-steel electrodes flush-mounted around the vessel periphery at 22.5° intervals. Figure 2 shows the cross-section of the stock chest and the location of the sensor planes. ERT is a noninvasive imaging technique which measures the distribution of electrical conductivity within a region of interest.14 Images were reconstructed using the linear back projection algorithm. To image the cavern, 80-120 conductive tracer particles were added to the pulp suspension immediately above the impeller. These particles, approximately 0.30 cm3 in volume (the size of a typical fiber floc), were neutrally buoyant and circulated within the cavern (which was identified as the region of higher conductivity in the tomographic images). Data acquisition was carried out for 15 min at each selected rotational speed to obtain 600 tomograms, which were averaged to obtain

Figure 2. Schematic of the cylindrical mixing chest showing ERT sensor planes (T ) 38.1 cm, Z ) 30.5 cm, C ) 12 cm, E ) 7 cm). The center lines of the planes P1, P2, P3, and P4 are 1.3, 9.5, 17.7, and 26 cm above the vessel base.

the cavern dimensions. The details of ERT measurement can be found in Hui et al.1

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Figure 3. NP vs Rey in a Cm ) 3% hardwood pulp suspension with NP measured to an average of (6% (side-entering configuration with D/T ) 0.4, E/D ) 0.4, C/D ) 0.7). In the laminar regime, the slope is -1, which is shown by a dotted line.

For a continuous flow chest, the time constant, which quantifies its dynamic response, is directly proportional to the cavern size. However we were concerned that under continuous flow conditions the flow rate through the chest would affect the cavern size. Hui et al.15 showed that cavern size is mainly a function of impeller speed and did not change significantly with a change in the flow rate through the chest. Although a slightly higher cavern size is expected in a continuously operated chest due to additional momentum imparted to the flow,15 our visual observations at Q ) 7 L/min indicated that the cavern boundaries along the chest walls and at the free surface were the same as in the batch operation. Hence, the dynamic tests were conducted at a fixed flow rate, Q ) 7 L/min. At this flow rate the theoretical time constant (V/Q) was about 5 min, and hence, the duration for a dynamic test was 40 min (about 8 times the theoretical time constant), giving sufficient data to estimate the mixing model and cavern size. The pulp suspension was pumped from a feed tank to the mixing chest and then to a discharge tank. The feed pipe extended down to the free surface of the suspension, while the discharge pipe was located on the side wall near the impeller. A predetermined pseudorandom binary signal was created by injecting a saline solution into the entering pulp stream.16 Conductivity variations in the input and output streams were measured (at 1 Hz), and the signals were analyzed to determine the mixing performance of the chest as detailed in Soltanzadeh et al.17 3. Results and Discussion 3.1. Measurements of Impeller Power Number and Axial Force Number. The variation of NP and Nf of the impellers as a function of yield stress Reynolds number (Rey ) FN2D2/τy) in a Cm ) 3% hardwood pulp suspension is shown in Figures 3 and 4. It is evident that the impellers were operating in the laminar and transition-to-turbulence regimes during the laboratory tests. The Maxflo impeller showed the lowest power number, followed by the A-312, marine propeller, and FF impeller. This dependence was correlated with the impeller pitch ratio, which was lowest for the Maxflo impeller (p/D ) 0.44), intermediate for the A-312 (p/D ) 0.9), and higher for the FF impeller (p/D ) 1.25). The pitch ratio for the marine propeller (p/D ) 1.5) was higher than that of the FF impeller, but it

Figure 4. Nf vs Rey in a Cm ) 3% hardwood pulp suspension with Nf measured to an average of (2% (top-entering configuration with D/T ) 0.6, C/D ) 0.6). In the laminar regime, the slope is -1, which is shown by a dotted line.

consumed less power above 500 rpm because of air entrainment from the suspension surface. An impeller with a higher pitch ratio is also expected to produce a larger axial flow, and the data for Nf above Rey ) 20 (Figure 4) reflects this. It is interesting to note that the Nf versus Rey plots show a minima for all the impellers tested except for the Maxflo impeller (perhaps due to the upper rotational speed available in the laboratory test apparatus). Similar behavior is also reported by Amanullah et al.10 for the axial flow SCABA 3SHP1 impeller operating in a 0.1 wt % Carbopol solution. These impeller performance numbers are important for predicting cavern size, as will be shown later. 3.2. ERT Measurement of Cavern Size. The typical power consumption for industrial agitated stock chests18 is 0.2-0.6 kW/m3. Figure 5 shows the tomographic images for the suspension agitated by different impellers at constant power consumption, P/V ) 0.53 kW/m3. The cavern corresponds to the high-conductivity regions in the images (red and green in the color reproductions) and did not fill the chest. The cavern boundary can be measured to within 5-10% of the chest diameter1 with the cavern boundaries at the vessel wall confirmed by visual observation. The cavern shape was determined using the cross-sectional images at each sensor plane, and it was found to be approximated by a cylinder truncated by the chest wall, as found by Hui et al.1 As the impeller speed was increased, the volume of the cavern grew. The onset of complete motion in the chest was defined as the condition at which the motion appeared everywhere on the free surface and along the (transparent) side walls, and it was monitored by visual observation. The complete motion on the free surface was attained before suspension motion completely filled the chest, as also noted by Ein-Mozaffari et al.19 Figure 6 shows the cavern geometry reconstructed from the ERT images for all impellers operating at constant power consumption, P/V ) 0.53 kW/m3. For the Maxflo impeller the cavern shape is a cylinder truncated by the chest walls, whereas with the other impellers, the shape diverges from cylindrical geometry. The cavern size appears to be larger on the topmost plane (P4). The ERT data for A-312 and FF impellers also show that a small region from plane P4 extended to the free surface immediately above the impeller is not a part of the cavern (Figure 6B and 6D). This region, although in motion (as


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Figure 5. ERT images obtained in the laboratory-scale chest for a Cm ) 3% hardwood pulp suspension at P/V ) 0.53 kW/m3 with the Maxflo (N ) 450 rpm), A-312 (N ) 425 rpm), marine propeller (N ) 355 rpm), and FF impeller (N ) 350 rpm). The impeller was located between planes 2 and 3 and electrodes 5 and 6 as shown for reference purposes in the upper left image.

Figure 6. Cavern shape (shaded volume) using ERT data for different impellers at P/V ) 0.53 kW/m3 in a Cm ) 3% hardwood pulp suspension: (A) Maxflo (N ) 450 rpm), (B) A-312 (N ) 425 rpm), (C) marine propeller (N ) 355 rpm), and (D) FF impeller (N ) 350 rpm).

observed visually), does not contain conductive particles and hence has limited connectivity with the cavern. The growth of the cavern with an increase in the impeller speed is shown in Figure 7 for the Maxflo impeller. The cavern boundary

propagates farther in the chest with an increase in the impeller speed. The cavern grows faster on the suspension surface than below it. Even when the complete motion appears on the top surface, the pulp is stagnant along the side wall opposite the

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Figure 7. Cavern shape (shaded volume) using ERT data for the Maxflo impeller operating at various speeds in a Cm ) 3% hardwood pulp suspension: (A) N ) 503 rpm (P/V ) 0.64 kW/m3), (B) N ) 552 rpm (P/V ) 0.90 kW/m3), and (C) N ) 605 rpm (P/V ) 1.1 kW/m3).

Figure 8. Cavern volume (measured using ERT) as a function of power per unit volume for side-entering impellers operating in a Cm ) 3% hardwood pulp suspension. The cavern volume is determined to (16%, as indicated by a representative error bar.

impeller. Visual observation confirmed this behavior for all the impellers tested. Additional measurements made varying the suspension height (Z/T ) 0.8-1.2) and using Maxflo impellers of different diameters (D/T ) 0.27, 0.37, and 0.43) also showed cavern growth completed on suspension surface first. Yackel’s mixing chest design procedure2 is based on achieving complete motion on the top surface of the chest, which does not ensure complete motion throughout the chest as seen in this work and also reported by Ein-Mozaffari et al.19 Cavern volume as a function of power consumption per unit volume is shown in Figure 8 for batch operation. Complete motion in the mixing chest is required for good mixing (determined from Figure 8 where Vc/V ) 1 and measured visually). The marine impeller required the greatest power to achieve complete motion due to air entrainment in the suspension, which impaired creation of motion in the chest. Air entrainment by the other impellers was also observed but only at power levels greater than that required to create complete suspension motion. The FF and A-312 impellers created complete motion at the lowest power consumption. In terms of torque requirements, the A-312 and Maxflo impellers were the most efficient (Figure 9) followed by the FF and marine impellers, respectively. The performance of the impellers in batch mode is included in Table 1 for P/V ) 0.53 kW/m3. At this specific power, the FF impeller created the largest cavern (Vc/V ) 0.66), followed by the marine and A-312 impellers (Vc/V ) 0.59 and 0.57), respectively, with the smallest cavern produced by the Maxflo impeller (Vc/V ) 0.47).

Figure 9. Cavern volume obtained using ERT as a function of torque per unit volume for side-entering impellers operating in a Cm ) 3% hardwood pulp suspension. Table 1. Model Parameters Obtained from Dynamic Tests Made on the Laboratory Chest for Agitation of a Cm ) 3% Hardwood Pulp Suspension with Different Impellers at P/V ) 0.53 kW/m3 and Q ) 7 L/mina impeller

Td (s)

τ1 (s)

τ2 (s)

f

VFM/V

Vc/V

Maxflo A-312 marine FF

85 ( 8 83 85 88

0 0 0 0

160 ( 15 164 193 198

0.04 0 0 0

0.51 ( 0.05 0.55 0.65 0.67

0.47 ( 0.08 0.57 0.59 0.66

a Fully mixed volume obtained from dynamic tests (VFM) for continuous operation is compared with the cavern volume (Vc) obtained from ERT in batch operation. Errors in the estimation of model parameters and cavern volume (by ERT) are given for the Maxflo impeller.

3.3. Analysis of Dynamic Mixing Tests. A continuous chest is expected to attenuate high-frequency variations entering it, with the time constant determining the frequencies affected. The dynamic model17 used to represent the cylindrical chest (Figure 10) divides the chest into two zones: a bypassing zone with time constant τ1 receiving fraction f of the total suspension flow, Q, and a well-mixed zone (corresponding to the mixed region agitated by the impeller) with time constant τ2 receiving the remaining flow, (1 - f)Q. The time delay associated with mixing chest, Td, is due largely to transport in the process piping between the conductivity sensors. The transfer function of the chest is given by G(s) )

(

)

1 - f -Tds f + e 1 + τ 1s 1 + τ2s

(3)


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Table 2. Time Constant and Fully Mixed Volume Obtained from Dynamic Tests with Different Impellers under the Conditions of Complete Motion (visually observed) for a Cm ) 3% Hardwood Pulp Suspension, Q ) 7 L/min, and the Nominal Time Constant, τ2 (ideal) ) V/Q ) 298 sa

Figure 10. Block diagram of the dynamic model for mixing in a stock chest (after Soltanzadeh et al.17).

impeller

N (rpm) (complete motion)

P/V (kW/m3)

τ2 (s)

VFM/V


640 550 605 453

1.29 1.09 1.93 1.04

256 ( 26 274 262 265

0.86 ( 0.09 0.92 0.88 0.89

a Errors in the estimation of time constant (and fully mixed volume) are given for the Maxflo impeller.

Figure 11. Typical inlet and outlet conductivities measured in a dynamic test and the predictions of the identified mixing model for the chest (eq 3) for a Cm ) 3%, hardwood pulp suspension agitated by aFF impeller at N ) 350 rpm and Q ) 7 L/min.

Figure 12. Effect of the D/T ratio of the Maxflo impellers (E/D ) 0.4) on power and torque requirements for complete motion (determined visually) in a Cm ) 3% hardwood pulp suspension in the laboratory chest.

with the fully mixed volume in the chest given by VFM ) τ2(1 - f)Q

(4)

VFM can be compared with the cavern volume obtained from ERT (Vc) in the batch operation. For proper identification of the model parameters used to determine VFM an excitation signal was provided by a series of step changes in the injection of a saline solution into the input pulp stream. The signal was designed to be rich in information so that the model parameters were identified accurately.17 Of the total data obtained in a dynamic test, the first half was used to estimate the mixing model and the remaining data was used for model validation. Typical variations in conductivity measured at the chest inlet and outlet during a dynamic test and the predictions of the identified mixing model are shown in Figure 11. Table 1 summarizes the results of dynamic tests made with all the impellers operating at a fixed power per unit volume of P/V ) 0.53 kW/m3. VFM (eq 4) is lowest for the Maxflo impeller and highest for the FF impeller and are similar (within experimental error) to that measured in batch operation using ERT. For the dynamic tests carried out in this work, the bypass fraction was negligible (f ≈ 0), which was attributed to the position of the chest outlet within the cavern zone. Also, the time delay identified, Td, was close to theoretical value of 82 s based on sensor location in the approach piping, the pipe dimensions, and the suspension flow rate, which confirms the robustness of the technique. Dynamic mixing tests were also carried out under conditions of complete suspension motion (as observed visually) in the chest. The measured time constants for the well-mixed region (τ2) reached about 90% of their theoretical values, as seen in Table 2. In other words, about 90% of the chest volume was involved in effective

mixing even though complete motion existed throughout it. However, the estimated standard deviation of model parameters indicates that the time constant (τ2) and hence the fully mixed volumes are accurate to (10%, indicating that the chest approached ideal mixing with the onset of complete motion in the laboratory chest. 3.4. Effect of Impeller D/T Ratio. An impeller with a large diameter operating at lower speeds is generally preferable for agitation of yield stress fluids.7,20 Using geometrically similar Maxflo impellers of different diameters (D ) 10.2, 14, and 16.5 cm) the conditions for complete motion in the chest were obtained from visual observation. With an increase in impeller diameter, the power requirement for complete motion decreased whereas the torque requirement increased, as shown in Figure 12. This is common behavior in fluid mixing operations.4 As the torque requirement relates to the capital cost of an installation (the cost of the impeller, shaft, and motor assembly) and the power requirement corresponds to the operating cost (electrical duty), the choice of an appropriate D/T ratio must be made considering the total fixed and variable costs for a given process. 3.5. Model Predictions for Cavern Sizes. The cavern sizes measured in this study were compared with predictions of the cavern model developed by Hui et al.1 According to this model, the following force balance is valid

[ ( )]

FN2D4 Nf2 +

4NP 3π

2 1/2

) τyS

(5)

The left-hand side is the net force generated by the impeller. The right-hand-side is the total resistive force at the cavern surface, which is the sum of the forces at the cavern-suspension surface,

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Figure 13. Comparison of cavern volume obtained from ERT and the predictions of the model by Hui et al.1 for a Cm ) 3% hardwood pulp suspension. Table 3. Characterization of Impellers at N ) 500 rpm in a Cm ) 3% Hardwood Kraft Pulp Suspension (corresponding to Rey ) 50) parameters impeller type

NP

Nf

KT


0.30 0.39 0.65 0.71

0.20 0.23 0.51 0.42

0.24 0.28 0.58 0.52

Sc, and at the cavern-wall surface, Sw. The force acting at the cavern-air interface was assumed to be zero. Hui et al.1 found that the suspension yield stress, τy, used in conjunction with the combined surface area (S ) Sc + Sw) gave the best prediction in their model. Knowing Np and Nf for the chosen impeller operating conditions (Cm and N) and the suspension yield stress (τy) permits the cavern surface area to be predicted and hence the cavern volume (once the cavern geometry is specified). In Figure 13, the predictions of this model are compared with the ERT (batch) data assuming right-cylindrical cavern geometry truncated by chest walls. The model captures the trends in the experimental data very well, particularly when allowance is made for experimental accuracy. The cavern volume can be measured to (16%, and for the Cm ) 3% hardwood pulp suspension the yield stress was measured to (22% (τy ) 38 ( 8 Pa). The accuracy of the yield stress measurement will affect the cavern size predicted by eq 5. The model underpredicts the power requirement for complete motion for the marine impeller because it does not account for air entrainment observed above N ) 500 rpm (which reduces suspension density and hence impeller power draw). In Figure 13, the model predictions for the FF impeller are based on an effective E/D ) 0.76 (E/D ) 0.4 was used for the other impellers). This accounts for the unique shape of the FF impeller, which has blades of ∼11 cm in length (see Figure 1D) that extend to the center axis of the chest when the shaft position is maintained at the same point as the other impellers. (The center of the FF impeller is effectively at 12.5 cm from the rear wall, even when the shaft overhang is 7 cm as in case of other impellers). In addition, the FF impeller sweeps out a considerably greater volume (1.6-4.8 times) compared with the other impellers, and hence, it creates larger cavern sizes at low N. From eq 5 it is clear that for a given impeller diameter impellers with greater values of NP and Nf are predicted to produce caverns with larger surface areas and hence larger volume. Table 3 compares these values and the term KT ) [Nf2 + (4Np/3π)2]1/2 for

each of the impellers studied. Here, NP, Nf, and KT were determined close to the transition-to-turbulence zone where industrial impellers usually operate (taken from Figures 3 and 4 at Rey ≈ 50. For industrial impellers, Rey ranges from 40 to 200). If we now compare KT for each impeller we find that for a given impeller diameter operated at a fixed speed that cavern size increases as KT increases, as expected (see Figure 13). However, to determine the most efficient impeller requires additional information (such as the ratio of impeller thrust to power input). Indeed, selecting the most effective impeller and operating conditions requires that the full model (eq 5) be used to evaluate a range of possibilities. Note that the model does not predict when an impeller will entrain air, as the marine propeller did, which requires additional information before making an impeller selection. In general, an axial flow impeller with high pitch is suitable for mixing of pulp fiber suspensions. The greater pitch ensures that NP is larger (Hemrajani and Tatterson21) and that Nf is greater too (as seen in this work). Thus, an impeller having a higher NP is not necessarily a penalty with respect to power consumption depending on the amount of flow created. Grenville and Nienow20 also recommend axial flow impellers with higher power number (e.g., pitched blade turbines) for the agitation of yield stress fluids. The mixing performance of axial flow impellers obtained in a cylindrical stock chest here would also be applicable for rectangular chests. While some changes in cavern volume may occur due to changes in the geometry, the trends in the cavern volume would remain the same. 4. Conclusions Four axial flow impellers of the same diameter were compared for their ability to create cavern volume in a Cm ) 3% pulp suspension under batch and continuous operation. With the exception of the marine propeller (which entrained air at higher rotational speeds), an axial flow impeller with the highest values of NP and Nf under the actual operating conditions was most energy efficient for creating cavern volume in the chest. The cavern volume measured using ERT for batch operation and the fully mixed volume measured using dynamic mixing tests for continuous operation (at Q ) 7 L/min) were found to be the same. The dynamic tests under conditions of complete motion in the chest (inferred from visual observations) gave about 90% fully mixed volume (measured to (10%), indicating that the chest approached ideal mixing with the onset of complete motion. The cavern volumes measured under batch operation were predicted within measurement accuracy by the cavern model developed by Hui et al.,1 which includes interaction between the cavern and the vessel walls. The model was not accurate when significant air was entrained by the impeller. Acknowledgment Thanks to NSERC, FPInnovations (Paprican Division), and the Dynamic Mixing Group at UBC (AbitibiBowater, Canadian Forest Products Ltd., Catalyst Paper Corporation, Domtar Inc., Entech/ Emerson Process Management, and Tolko Industries Ltd.) for financial support. Thanks also to Afromix, Chemineer, and Philadelphia Mixing Solutions for supplying the laboratory-scale impellers. Notation C ) impeller clearance from bottom (m) Cm ) mass concentration of fibers or consistency (%) D ) impeller diameter (m) E ) impeller clearance from rear wall (cm)

Ind. Eng. Chem. Res., Vol. 49, No. 9, 2010 f ) bypass fraction in mixing model defined by eq 3 (-) FA ) axial force of impeller (N) G ) transfer function of chest [eq 3] KT ) a term in the square bracket in eq 5, [Nf2 + (4Np/3π)2]1/2 (-) M ) shaft torque (N · m) N ) rotational speed of impeller (rpm) Nf ) axial force number of impeller defined by eq 2 (-) NP ) power number of impeller defined by eq 1 (-) p ) impeller pitch (m) P ) power consumption by impeller (kW) Q ) suspension flow rate (L/min) Rey ) yield stress Reynolds number, FN2D2/τy (-) Sc ) surface area of cavern in contact with suspension (m2) Sw ) surface area of cavern in contact with walls (m2) T ) diameter of cylindrical chest (m) Td ) time delay in mixing model [eq 3] (s) V ) pulp suspension volume (m3) Vc ) cavern volume (m3) VFM ) fully mixed chest volume (m3) Z ) height of pulp suspension in chest (m) Greek Letters F ) density of pulp suspension (kg/m3) τ1 ) time constant of bypass zone in mixing model [eq 3] (s) τ2 ) time constant of well-mixed zone in mixing model [eq 3] (s) τy ) yield stress (Pa)

Literature Cited (1) Hui, L. K.; Bennington, C. P. J.; Dumont, G. A. Cavern formation in pulp suspensions using side-entering axial-flow impellers. Chem. Eng. Sci. 2009, 64, 509. (2) Yackel, D. C. Pulp and Paper Agitation: The History, Mechanics, and Process; TAPPI Press: Atlanta, 1990. (3) Foxall, R. Basic concepts affecting agitation in stock preparation. TAPPI Papermakers Conference, Seattle, April 8-10, 1991; p 543. (4) Oldshue, J. Fluid Mixing Technology; McGraw Hill: New York, 1983. (5) Ein-Mozaffari, F.; Bennington, C. P. J.; Dumont, G. A. Dynamic mixing in industrial agitated stock chests. Pulp Paper Can. 2004, 105, 41.

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ReceiVed for reView November 23, 2009 ReVised manuscript receiVed March 9, 2010 Accepted March 13, 2010 IE901854D

Performance of Four Axial Flow Impellers for Agitation of Pulp

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