Optimization and Management of Flotation Deinking Banks by Process

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Ind. Eng. Chem. Res. 2009, 48, 3964–3972

Optimization and Management of Flotation Deinking Banks by Process Simulation Davide Beneventi,*,† Elisa Zeno,‡ Patrice Nortier,† Bruno Carre´,‡ and Gilles Dorris§ Laboratoire de Ge´nie des Proce´de´s Papetiers (LGP2), UMR CNRS 5518, Grenoble INP-Pagora 461, rue de la papeterie, 38402 Saint-Martin-d’He`res, France, Centre Technique du Papier (CTP), DU, BP 251, 38044 Grenoble CEDEX 9, France, and FPInnoVations, 570 Saint Jean BouleVard, Pointe-Claire, Quebec, Canada, H9R 3J9

In this work, the contribution of flotation deinking banks design on ink removal efficiency, selectivity, and specific energy consumption was simulated using a semiempirical approach. Single-stage with mixed tank/ column cells, two-stage, and three-stage configurations were evaluated, and the total number of flotation units in each stage and their interconnection were used as main variables. Explicit correlations between ink removal efficiency, selectivity, energy consumption, and line design were developed for each configuration. When considering a conventional two-stage configuration as reference, a decrease in the specific energy consumption for constant ink removal efficiency and selectivity was obtained with the single-stage bank with a stack of flotation columns at the front of the line, whereas an increase in ink removal selectivity for constant ink removal efficiency and specific energy consumption was obtained with the three-stage bank. The present results show that the performance of conventional flotation deinking banks can be improved by optimizing process design and implementing mixed tank/column technologies in the same deinking line. 1. Introduction 1

Recent statistics show that the use of recovered papers for newsprint and graphic papers manufacturing increased steadily in the last 14 years. In 2007, the growth of recovered fibers in the world, as a papermaking furnish, exceeds that of virgin fibers. Indeed, recovered paper already surpasses wood as the primary source of fibers for the manufacturing of paper and paperboard. However, the progressive improvement of DIP quality, i.e., low residual ink and visible ink dots, has been obtained by increasing the number of unit operations in industrial deinking lines at the expense of process simplicity and low energy consumption. In the new era of energy rationalization and use of renewable energy sources, the environmental impact of recovered papers deinking is questioned.2 Indeed, the use of recovered celluloses fibers (RCF) for the production of biofueland carbohydrate-based chemicals3,4 is becoming a possible alternative to RCF use in papermaking. Thereafter, the improvement of the flotation deinking operation toward lower energy consumption and higher separation selectivity appears to be necessary for a sustainable use of RCF in papermaking. The focus of current research activities in the world is no longer in making radical changes in deinking technology and/ or in intensifying the number of unit operations in the deinking process. Though there is still room for such activities, the current state of the paper industry dictates that most effort be devoted to reduce cost by optimizing the design of flotation units/banks and the use of deinking, flotation, and bleaching additives. The influence of physicochemical parameters on the froth flotation process has been extensively investigated in the past decade. Detailed mechanistic models are now available to describe the collection of hydrophobic particles by air bubbles and particle transport in the froth.5-7 In the minerals processing * To whom correspondence should be addressed. Tel.: +33 4 76 82 69 54. Fax: +33 4 76 82 69 33. E-mail: [email protected]. † Laboratoire de Ge´nie des Proce´de´s Papetiers. ‡ Centre Technique du Papier. § FPInnovations.

field, a mapping of particle collection and water distribution inside a flotation cell has been obtained by CFD modeling,8,9 and a number of models to optimize the design of flotation banks can be found in the literature.10-12 In the flotation deinking field, modeling approaches based on neural networks analysis13 and on semiempirical correlations14 have been recently proposed for single flotation units and conventional two-stage banks, respectively. Despite significant progress, process simulation to correlate flotation deinking banks design and their performance has not yet reached its full potential, and most of the guidelines recommended in the literature for the optimization of flotation banks in minerals flotation cannot be directly applied to deinking systems. The aim of our work is to provide a comprehensive understanding on the contribution of process design on ink separation selectivity and energy consumption. As a step in this direction, we evaluated the effect of adding two additional stages to a single-stage flotation with number of flotation cells in each stage being used as the main variable. The use of flotation columns to improve ink removal and reduce specific energy consumption15,16 was also simulated. 2. Simulation of the Flotation Deinking Process 2.1. Simulation of Particle and Water Transport. Particle and water transport during flotation deinking were simulated using semiempirical equations proposed and validated in previous works.14,17,18 The flotation process is described in terms of flotation, entrainment, frothing, and water/particle drainage in the froth. Transport coefficients to run simulations were obtained for a model pulp by fitting previously obtained laboratory data with transport equations,17 accounting for chemical effects induced by changes in surfactant concentration. The composition of the model pulp before flotation is given in Table 1. Model equations were entered in process simulation software (CadSim Plus 2.4), which was used to run mass balance calculations involving multistage systems and to compute

10.1021/ie801753j CCC: $40.75  2009 American Chemical Society Published on Web 03/20/2009

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recirculated at the inlet of the second stage in order to stabilize the pulp flow at 40 m3/min. The number of flotation tanks in the first and second stage was used as the main variable to optimize the line design. In a previous study,14 we showed that ink removal selectivity with respect to cellulose fibers and fine elements may be improved by adding a third stage to conventional two-stage lines. Moreover, simulation was previously run without accounting for progressive accumulation of surfactant in the second and third stage17 with the ensuing decrease in the ink removal efficiency.20 In the simulations, surfactant transport was taken into account because it affects particle and water transport in each flotation cell. The three-stage line was made of a first stage with 7-8 flotation tanks, a second stage with 2 tanks, and a third stage with 1 tank. As illustrated in Figure 2b, the pulp processed in the third stage was partitioned between the inlets of the third and second stage. The pulp processed in the second stage was partitioned between the inlets of the second stage itself and of the first stage. In order to limit the number of variables, all simulations were run with zero froth retention time. Under this condition, ink removal and fiber/fillers loss are maximized because particle and water drainage phenomena from the froth to the pulp are suppressed, but this is obtained at the expense of ink removal selectivity.17 Simulation results are therefore representative of deinking lines operated at their maximal ink removal capacity. 2.3. Assessment of Deinking Line Performance. The performance of simulated deinking lines was evaluated using pulp flows and the concentration of each particle class. Ink, fiber, and ash removal (IR, FR, AR) were calculated by direct mass balance

Table 1. Consistency and Composition of the Pulp Slurry Feeding the Deinking Linea consistency (g/L)

ERIC (ppm)

ink (%)

fiber (%)

fines (%)

ash (%)

surfactant (µM)

10

827

2.1

57.6

22.3

20.1

5

a

ERIC represents the pulp residual ink content as determined by light reflectance measurement.

transport coefficients for a predetermined surfactant concentration at the inlet of each flotation cell in multistage systems. 2.2. Flotation Deinking Banks. In order to clarify the contribution of multistage deinking lines design on ink removal and process yield, six bank configurations of increasing complexity were modeled. As summarized in Table 2, flotation banks were assembled using flotation cells with two different aspect ratios, 0.7 for the tank cell, 2 for the column cell, and with a constant pulp capacity of 20 m3. With both cell geometries, pulp aeration was assumed to take place in Venturi aerators with an aeration rate Qg/Qpulp ) 0.5 and a pressure drop of 1.2 bar.19 Tank and column cells were assumed to be equipped with one and two aerators, respectively. To run simulations under realistic conditions, the superficial gas velocity in a single-column cell was set at 2.4 cm/s, which corresponds to an air flow rate of 10 m3/min or one-half that in the tank cell. Similarly, the pulp flow processed in flotation columns was limited to a maximal value of 10 m3/min. Figure 1 illustrates the four single-stage lines simulated in this study. The first case in Figure 1a consists in a simple series of flotation tanks, with common launder collecting flotation froths from each cell to produce the line reject. The number of tanks was varied from 6 to 9. With the aim of limiting fiber loss and maximizing ink removal rate at the front of the line, rejects of flotation cells at the end of the line were cascaded back at the line inlet (Figure 1b) while froth rejected from the first few cells was rejected. Using this configuration, the simulation was carried out with the number of tanks in the line and cascaded reject flows being used as main variables. In the third configuration, the pulp retention time at the head of the line was doubled by placing two tanks in parallel followed by a series of 7 tanks whose rejects were returned at the line inlet (Figure 1c). The last singlestage configuration consisted in a stack of 4-6 flotation columns in parallel, followed by a series of 3-5 tanks whose rejects were sent back to the line inlet (Figure 1d). The aim of this configuration was to increase ink concentration and pulp retention time at the head of the line and to assess the potential of column flotation for ink removal efficiency. As depicted in Figure 2, two- and three-stage deinking lines were also simulated. The two-stage line (Figure 2a) is the most widely used one in flotation deinking.17 In this classical configuration, reject of the first stage (also denoted the primary, or 1ry, line), are generated in 5-9 primary cells in series. To recover valuable fibers in these combined reject stream, rejects of the primary line are processed in a second stage (also denoted the secondary, or 2ry, line) with 1-4 tanks. Generally, a fraction of the accept pulp of the second stage, ∼20%, is returned to the inlet of the first stage while the remaining fraction is

IR )

out Qincin ink - Qoutcink

(1)

Qincin ink

in out , cink are the pulp flow and ink where Qin, Qout and cink concentration at the inlet and oulet of the deinking line, respectively. The fiber and ash removal were calculated using the corresponding concentrations at the line inlet and outlet. The residual ink (ERIC)21 in processed pulp was calculated by using the equation

ERIC )

cinkrref cpulprink

(2)

where cink is the ink concentration in the pulp, cpulp the pulp concentration, rink the average radius of ink particle after alkaline pulping of a conventional old newsprints/old magazines mixture,22 and rref the average radius of reference ink particles, viz. ∼13 and 0.5 µm, respectively. Residual ink in pulps is indirectly evaluated by measuring pulp light reflectance at 950 nm and converting it into an equivalent ink weight fraction by using the light absorption coefficient of a reference, finely dispersed, black ink. The large difference existing between the size of ink particles dispersed in the pulp slurry and the reference ink would lead to an underestimation of the ERIC. The rref/rink ratio was

Table 2. Relevant Characteristics of Flotation Units Used To Assemble the Flotation Lines Simulated in This Study flotation unit

pulp volume (m3)

cross section (m2)

aspect ratio h/d

pulp feed flow (m3/min)

air flow (m3/min)

superficial gas velocity (cm/s)

gas hold-upa (%)

ink flotation rate constant (1/min)

ink removal (%)

tank column

20 20

12 7

∼0.7 ∼2

40 40/m*

20 10

2.8 2.4

10-20 30-40

∼0.45 ∼0.52

20-35 50-65

a

Estimated assuming a bubble slip velocity relative to the pulp downstream flow of ∼7 cm/s.

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therefore used in eq 2 to account for this size difference and to calculate ERIC using ink concentrations obtained from mass balance. The deinking selectivity factor (Z)23 of ink particles with respect to fibers was also calculated as the ratio between ink and fiber removal Z)

IR FR

(3)

In deinking lines using Venturi aerators, most of the energy required for pulp processing is consumed during the aeration stage. Indeed, the whole pulp stock is pumped in aerators generating a pressure drop from 0.9 to 1.5 bar.19 In order to compare on a relative scale the energetic performance of simulated lines, the hydraulic specific energy (SE) needed to process the pulp stream in the flotation line was calculated as

SE )

Pinj

∑

n

Qg

RQoutcout

(4)

where Qg is the gas flow injected in each flotation cell (n) in the multistage system, Pinj is the pressure feed of each static aerator (1.2 bar), R is the aeration rate Qg/Qpulp (0.5 in the simulated conditions), and Qout and cout are the pulp volumetric

Figure 2. Multistage flotation lines simulated in this study. (a) Conventional two-stage line with n cells in the primary stage and m cells in the secondary stage. (b) Three-stage line with n ) 8 and m ) 2.

Figure 3. Ink removal (IR) and residual ink content (ERIC) in floated pulp obtained for flotation lines shown in Figure 1a and 1b and composed by a series of 6-9 flotation cells.

flow and consistency at the outlet of the deinking line, respectively. 3. Results and Discussion

Figure 1. Single-stage flotation lines simulated in this study. (a) Simple line made of a series of n flotation cells. (b) Line with n flotation cells with the reject of the last n - m cells cascaded back at the line inlet. (c) Line composed by n flotation cells with the first two cells in parallel and the remaining cells in series. The reject of the last n - 2 cells is cascaded back at the inlet of the line. (d) Deinking line composed by a stack of m flotation columns in parallel and a series of n cells. The reject of flotation cells is cascaded back at the inlet of the line.

3.1. Single-Stage Deinking Lines. Figure 3 shows that, in the absence of reject recirculation (i.e., 0 cascaded cell), raising the number of flotation tanks progressively increased ink removal from 82% to 94%, whereas the residual ink content (ERIC) decreased from 250 to 95 ppm. On the other hand, 12% gain in ink removal was accompanied by 14% increase in fiber removal (Figure 4a) and the specific energy consumption doubled (Figure 4d). These simulation results support industrial practice24 that single-stage deinking lines (with tank cells), without flotation rejects reprocessing, are unsuitable because

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Figure 4. Fiber (a), ash (b), and total solids (c) removal and specific energy consumption (d) obtained for flotation lines shown in Figure 1a and 1b.

high ink removal is accompanied by poor yield and excessive specific energy consumption. Figure 3 shows that returning flotation rejects at the line inlet decreased ink removal progressively as the number of cascaded cells increased. Whatever the number of tanks in the line, ink removal deteriorated when the ratio between the number of cascaded cells and the number of cells in the line (cascade ratio) was higher than 0.6. Above this critical value ink started to build up in the line because flotation tanks at the head of the line were no longer able to counterbalance the increase in ink concentration induced by the return of flotation rejects. As shown in Figure 4b, the cascade ratio produced a similar trend on ash removal. The removal of cellulose fibers displayed a quasi linear decrease, Figure 4a, at increasing cascade ratios. The different shape of ink/ash removal and fiber removal curves originates from the different transport mechanisms of the various pulp constituents. Ink and ash particles are removed by true flotation whereas fibers are transported to the froth by entrainment. Because of first-order kinetics, removal of hydrophobic particles obviously improves at longer retention times but is it independent of initial particles concentration. Conversely, the degree of particle entrainment is mainly correlated to the water volume in the reject flow. Figures 3 and 4 show that for cascade ratios below 0.6, the increase of the number of flotation rejects cascaded back at the line head induced a significant increase in the ink removal selectivity with respect to cellulose fibers. Indeed, whatever the total number of flotation tanks in the line, a 10-24% decrease in fiber removal was accompanied by only a 6-10% decrease in ink removal. For a fixed number of flotation tanks, the pulp processing capacity progressively decreased when increasing the cascade ratio. Because the yield increase counter balanced this loss in ink removal, the pulp production capacity remained almost unchanged and the specific

Figure 5. Ink removal and residual ink content in floated pulp obtained for flotation lines shown in Figure 1c and 1d.

energy consumption slightly decreased (Figure 4d). In order to increase ink removal when cascading flotation rejects, pulp retention time and ink removal efficiency at the line head were increased by arranging flotation cells in parallel and by replacing the tank with column cells, respectively (Figure 1c and 1d). With a total number of 9 tank cells in the line, ink removal increased from 63.6% to 79.5% when disposing two tanks in parallel at the line head (Figure 5). However, ink removal and yield were similar to those obtained with a series of 9 flotation cells with the reject of the last 7 cells cascaded back at the inlet of the line (Figures 3 and 4). The gain in ink removal was due

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Figure 6. Total solids removal and specific energy consumption of the flotation lines shown in Figure 1c and 1d.

Figure 8. Ink removal (IR) and residual ink content (ERIC) in floated pulp obtained for the flotation line shown in Figure 2a as a function of the number of flotation cells in the primary (1ry) and secondary (2ry) stage.

Figure 7. Fiber and ash removal obtained for the flotation lines shown in Figure 1c and 1d.

to an increase in the flotation reject and not to an increase in ink removal selectivity. Figure 5 shows that when arranging four column cells in parallel at the line head, ink removal increased from 63.6% to 85.3% and the specific energy consumption dropped from 56 to 43 kWh/t (Figure 6). This efficiency gain is caused by the higher ink removal efficiency of column cells when compared to tank cells (Table 2). As observed before, better ink removal was accompanied by a corresponding increase in fiber and ash removal, as shown in Figures 6 and 7. The further increase of the number of columns and of tanks gave a substantial increase in ink removal efficiency which reached 92%. However, ink removal selectivity did not increase and the process yield dropped to 85.3% and 61% for fiber and total solids, respectively (Figures 5-7). All tested configurations clearly demonstrate that high ink removal can be attained with single-stage deinking lines. However, for a reference ink removal target of 80%, the low selectivity of ink removal with respect to mineral fillers and fibers generates excessive fiber and total solids removal, i.e., ∼15% and ∼30%, respectively. Additional simulations showed that ink removal selectivity increased when increasing the froth retention time. Nevertheless, whatever the line and flotation cell design, the removal of cellulose and mineral fillers remains too high, showing that froth washing25,26 or a second flotation stage are needed to obtain an acceptable process yield.

3.2. Multistage Deinking Lines. Simulation results obtained for two-stage deinking lines plotted in Figure 8 show that, independently from the number of cells in the second stage, ink removal increased from 69% to 81% and 89% when increasing the number of primary flotation tanks from 5 to 7 and 9, respectively. The effect of additional cells in the second stage on ink removal is less pronounced than in the first stage. As indicated in Figure 8, adding a second, third, and fourth cell enhanced ink removal by 13%, 4%, and 2%, respectively. Figure 9a shows that a similar trend was obtained for floatable mineral fillers, whereas fiber removal increased by 5% for each additional cell. This behavior is ascribed to the increase in the reject flow due to the addition of flotation cells in the second stage and to the associated increase in fiber removal by entrainment.27 Results presented in Figures 8 and 9 are clear illustrations that an increase of the number of primary cells always improves the removal of floatable particles, i.e., ink and mineral fillers. Raising the number of cells in the second stage improves ink removal with a plateau effect after two cells and with ever increasing fibers and total solids removal. Present results show that in a two-stage deinking line, ink and mineral fillers removal targets dictate the number of cells in the first stage, whereas the number of cells in the second stage is chosen to get the best compromise between ink and fiber removal. Our simulations show that two secondary cells are sufficient to optimize ink removal and yield loss. Upon the addition of a single flotation cell as a third stage of a two-stage deinking line, the fiber removal decreased from 8.5% to 3.3% and ink removal from 80.9% to 76.5% (Figure 10), respectively. As shown in Figures 10 and 11, the slight loss in ink removal due to the addition of the third stage was recovered by installing an additional cell in the first stage without affecting fiber and total solids removal. Despite an increase in the complexity of the deinking line, Figure 11 shows that threestage lines had lower specific energy consumption and better yield than two-stage lines. 3.3. Specific Energy Consumption and Deinking Selectivity. Flotation lines assembled here for simulation purposes were characterized by a fixed (tank cells) and an adjustable (column cells) feed flow. As the introduction of

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Figure 10. Ink (a) and fiber and ash (b) removal obtained for 3-stage flotation line shown in Figure 2b. Removal efficiencies are compared with those obtained for a standard 2-stage line with 7 cells in the 1ry stage and 2 cells in the 2ry stage.

Figure 9. Ash and fiber removal (a) and total solids removal and specific energy consumption (b) obtained for the flotation line shown in Figure 2a and plotted as a function of the number of flotation cells in the 1ry and 2ry stage.

recirculation loops modifies the processing capacity and the pulp retention time in the whole line, predicting particle removal efficiencies is not sufficient to establish a performance scale between different configurations. Consequently, specific energy consumption, ink removal efficiency, and ink removal selectivity have to be taken into account to establish a correlation between process efficiency and line design. Figure 12a illustrates that when the cascade ratio is raised in single-stage lines, the deinking selectivity (Z) increased by 4-5 times whereas the specific energy consumption slightly decreased. Reduced energy is caused by a net increase in pulp production capacity. However, these gains were generally associated with a decrease in ink removal. Hence, the reference

Figure 11. Total solids removal and specific energy consumption obtained for the 3-stage line shown in Figure 2b. Data are compared with those obtained for a standard 2-stage line with 7 cells in the 1ry stage and 2 cells in the 2ry stage.

target of 80% ink removal with a selectivity factor Z ) 8 could only be obtained with a line made of 9 tanks with a cascade ratio of 0.6 and a specific energy consumption of 60 kWh/t. Because target ink removal and selectivity can be achieved only

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Figure 12. Ink removal efficiency (IR) and selectivity (Z) obtained for tested configurations plotted as a function of the specific energy consumption. (a) Flotation line composed by 6-9 flotation cells and with the reject of the last n - m cells cascaded back at the line inlet (Figure 1a and 1b). (b) Flotation line composed by a stack of flotation cells or columns in parallel followed by a series of flotation cell (Figure 1c and 1d).

Figure 13. Ink removal efficiency (IR) and selectivity (Z) obtained for tested configurations plotted as a function of the specific energy consumption. (a) Deinking line composed by a 1ry and a 2ry stage with different number of flotation cells in the two stages (Figure 2a). The legend in the pictures indicates the number of cells in the 1ry stage. (b) Line of 3 stages (Figure 2b).

by increasing energy consumption, this configuration does not represent a real gain in terms of process performance. The addition of a high ink removal efficiency stage comprising a stack of flotation columns in parallel at the line head, Figure 12b, reduced specific energy consumption by 25-50%. Nevertheless, the efficient removal of floatable mineral fillers and the absence of hydrophilic particle drainage in the froth limited the selectivity factor to ∼7.5. According to experimental studies,22,25,28 the increase of the froth retention time and the implementation of a froth washing stage would improve the selectivity factor with a minimum loss in ink removal. Under these conditions, a flotation columns stack equipped with optimized froth retention/washing systems would markedly decrease specific energy consumption. Similar to the results obtained for single-stage lines, Figure 13a shows that improved ink removal selectivity in two-stage lines is coupled with a decrease in ink removal. The selectivity factor appears to be directly correlated to the number of flotation tanks in the secondary line as it progressively decreased from ∼17.5 to 5 when increasing the number of tanks in the second

stage. Selectivity dropped when the reject flow increased which, for two- and single-stage lines, is induced by the increase of the number of tanks in the second stage and the decrease of the cascade ratio, respectively. In turn, ink removal efficiency was found here to be governed by the number of cells in the first stage. Figure 13a shows that with a constant number of tanks in the second stage, ink removal increased by 10% for each additional cell in the first stage, while selectivity slightly increased. Seven tanks in the first stage and two tanks in the second stage are needed to reach the target of 80% ink removal and a selectivity factor of 9. With this configuration, the specific energy consumption of the two-stage line (52 kWh/t) is lower than the energy required by a single-stage line with the same deinking efficiency/selectivity (60 kWh/t). Overall, the best energetic efficiency is given by the single line with a stack of six flotation columns at the line head (Figure 12b). If we consider the two-stage line with ink removal and selectivity targets as a reference system, the addition of a third stage with a single tank boosted up selectivity, slightly decreased ink removal from 81% to 78%, and did not affect specific energy

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The addition of a third stage allowed increasing ink removal selectivity with a negligible effect on the ink removal efficiency and the specific energy consumption. Among the tested configurations the single-stage bank with a stack of flotation columns at the line head and the three-stage bank gave the most promising results, reducing specific energy consumption for constant ink removal efficiency and selectivity. Appendix: Particle and Water Transport Mass transfer in the flotation deinking process was modeled using well-established correlations applied in minerals flotation8,29,30 whose validity for flotation deinking systems has been verified in previous studies.17,18 The removal of hydrophobic materials by adhesion at the surface of air bubbles was described using a first-order kinetic equation dcfn ) -kncn dt

Figure 14. Visual representation of the equation system used to model mass transport in a single flotation cell.

consumption (Figure 13b). The selectivity index of the threestage line can be further increased from 21.5 to 41 by setting at 16 s froth residence time in the third-stage cell. However, the selectivity gain was coupled to a decrease in ink removal from 78% to 72% and the need for an additional tank in the first stage to attain the ink removal target of 80%. With this last configuration of 8 tanks in the first stage, 2 tanks in the second stage, and 1 tank in the third stage, 80% ink removal was attained along the highest selectivity factor of all tested configurations. However, the gain in separation efficiency resulted in a sizable increase in the specific energy consumption. As for the other tested configurations, the effective benefit provided by this configuration should be thoroughly evaluated in the light of recovered papers, rejects disposal, and energy costs. 4. Conclusions The layout of flotation banks was progressively upgraded from single-stage, with flotation tanks and columns, to two- and three-stage design and simulation results showed the following. In single-stage banks, ink removal selectivity and specific energy consumption can be improved by increasing the cascade ratio (i.e., the ratio between the number of cascaded cells and the total number of cells in the line) up to ∼0.6 with a minimum decrease in the ink removal efficiency. Above this threshold, ink removal efficiency dropped and ink particles started to build up in the line. The addition of a stack of flotation columns in the head of a single-stage line gave an increase in ink removal efficiency, selectivity, and a general decrease in specific energy consumption. In two-stage banks, the ink removal efficiency was mainly affected by the number of flotation tanks in the first stage, whereas the number of cells in the second stage affected the fiber removal, which linearly increased with the number of cells. For all tested two-stage banks and whatever the number of cells in the first stage, the best compromise between ink removal, selectivity, and specific energy consumption was obtained with two cells in the second stage.

(5)

where cn is the concentration of the substance in class n (namely, ink, ash, organic fine elements, cellulose fines, and surfactant) and kn is its corresponding flotation rate constant kn )

KnQg S

(6)

where Qg is the gas flow, S is the cross-sectional area of the flotation cell, and Kn is an experimentally determined parameter including hydrodynamic and physicochemical factors affecting bubble/particle interactions.17,18 Particles and solutes entrainment in the wake of air bubbles was correlated to their concentration in the pulp slurry and to the water upward flow in the froth. The variation in concentration due to entrainment was given by the equation φQ0f dcen )c dt V n

(7)

where φ ) c0f /cn is the entrainment coefficient, Qf0 is the water upward flow in the froth in the absence of drainage, c0f is the particle concentration at the pulp/froth interface, and V is the pulp volume in the flotation cell. The total variation of particles/ solutes concentration due to flotation and entrainment was given by the sum of the two contributions, i.e., dcn/dt ) dcfn/dt + dcen/dt. Water drainage through the froth was described using water hold up in the froth (ε) and froth retention time (FRT) in the flotation cell as main parameters ε)

Qf Qf + Qg

FRT )

h Jg + jJf

(8)

(9)

where Qg and Qf are the gas and froth reject flows, h is the froth thickness, and Jg and Jf are the gas and water superficial velocities in the froth. The decrease of the water hold up in the froth versus the FRT was described by the usual exponential decay29,30 ε ) ε0e-Ld · FRT

(10)

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where ε0 is the water volume fraction at the froth/pulp interface and Ld is the water drainage rate constant. The drainage flow of particles and solutes dispersed in the froth, dMf /dt, was given by the equation dMf ) -δcnfQd dt

(11)

where Qd is the water drainage flow, δ ) cd/cnf is the particle drainage coefficient, and cnf and cd are the particle concentration in the froth and in the water drainage stream, respectively. To solve the equations system, perfect mixing and piston flow were assumed to occur in the aerated pulp and in the froth. A scheme of the flotation process and of variables used to simulate particle transport is shown in Figure 14. Literature Cited (1) Confederation of European Paper Industries, Special Recycling 2005 Statistics. CEPI, http://www.cepr.org/, Brussels (2006). (2) Bystro¨m, S.; Lo¨nnstedt, L. Paper recycling: a discussion of methodological approaches. Resour. ConserV. Recycl. 2000, 28 (1), 55–65. (3) Hunter, N. Fuel plus from the forest: a short review and introduction to the biorefinery concept. Appita J. 2007, 60 (1), 10–12. (4) Sjoede, A.; Alriksson, B.; Joensson, L. J.; Nilvebrant, N.-O. The potential in bioethanol production from waste fiber sludges in pulp millbased biorefineries. Appl. Biochem. Biotechnol. 2007, 137-140 (1-12), 327–337. (5) Bloom, F. A mathematical model of continuous flotation deinking. Math. Comp. Model. Dyn. Sys. 2006, 12 (4), 277–311. (6) Bloom, F.; Heindel, T. J. Modeling flotation separation in a semibatch process. Chem. Eng. Sci. 2003, 58 (2), 353–365. (7) Neethling, S. J.; Cilliers, J. J. Solids motion in flowing froths. Chem. Eng. Sci. 2002, 57 (4), 607–615. (8) Koh, P. T. L.; Schwarz, M. P. CFD modelling of bubble-particle collision rates and efficiencies in a flotation cell. Miner. Eng. 2003, 16 (11), 1055–1059. (9) Herbst, J. A.; Potapov, A. V.; Pate, W. T.; Licher, J. K. Advanced modelling for flotation process simulation. Centenary of Flotation Symposium, Brisbane, QLD, June 6-9, 2005; pp 111-119. (10) Neethling, S. J.; Cilliers, J. J. The simulation of flotation banks and circuits. Centenary of Flotation Symposium, Brisbane, QLD, June 69, 2005; pp 153-158. (11) Cisternas, L. A.; Mendez, D. A.; Galvez, E. D.; Jorquera, R. E. A MILP model for design of flotation circuits with bank/column and regrind/ no regrind selection. Int. J. Miner. Process. 2006, 79 (4), 253–263. (12) Hulbert, D. G. The optimum distribution of cell capacities in flotation circuits. Miner. Eng. 2001, 14 (5), 473–486. (13) Labidi, J.; Pelach, M. A.; Turon, X.; Mutje´, P. Predicting flotation efficiency using neural networks. Chem. Eng. Process. 2007, 46 (4), 314– 322.

(14) Beneventi, D.; Benesse, M.; Carre´, B.; Julien Saint Amand, F.; Salgueiro, L. Modelling deinking selectivity in multistage flotation systems. Sep. Purif. Technol. 2007, 54 (1), 57–67. (15) Chaiarrekij, S.; Dhingra, H.; Ramarao, B. V. Deinking of recycled pulps using column flotation: energy and environmental benefits. Resour. ConserV. Recycl. 2000, 28 (3-4), 219–226. (16) Hernandez, H.; Gomez, C. O.; Finch, J. A. Gas dispersion and deinking in a flotation column. Miner. Eng. 2003, 16 (8), 739–744. (17) Beneventi, D.; Allix, J.; Zeno, E.; Nortier, P. Influence of surfactant concentration on the ink removal selectivity in a laboratory flotation column. Int. J. Miner. Process. 2008, 87 (3-4), 134–140. (18) Beneventi, D.; Allix, J.; Zeno, E.; Nortier, P.; Carre´, B. Simulation of surfactant contribution to ink removal selectivity in flotation deinking lines. Sep. Purif. Technol. 2009, 64 (3), 357–367. (19) Kemper, M. State-of-the-art and new technologies in flotation deinking. Int. J. Miner. Process. 1999, 56 (1-4), 317–333. (20) Beneventi, D.; Zeno, E.; Carre´, B.; Allix, J.; Nortier, P.; Angelier, M. C. Understanding the role of surface active substances in flotation deinking mills by coupling surfactant and ink balance with process simulation. Prog. Paper Recycl. 2008, 18 (1), 31–39. (21) Jordan, B. D.; Popson, S. J. Measuring the concentration of residual ink in recycled newsprint. J. Pulp Paper Sci. 1994, 20 (6), 161–167. (22) Beneventi, D.; Rousset, X.; Zeno, E. Modelling transport phenomena in a flotation de-inking column. Focus on gas flow, pulp and froth retention time. Int. J. Miner. Process. 2006, 80 (1), 43–57. (23) Zhu, J. Y.; Tan, F.; Scallon, K. L.; Zhao, Y. L.; Deng, Y. Deinking selectivity (Z-factor): a new parameter to evaluate the performance of flotation deinking process. Sep. Purif. Technol. 2005, 43 (1), 33–41. (24) Dreyer, A.; Britz, H.; Renner, K.; Heikkila¨, P.; Grimm, M. Circuit designs for secondary accept in deinking flotation. Proceedings of the 13th PTS-CTP Deinking Symposyum, April 15-17, 2008, Leipzig, Germany; p 16. (25) Robertson, N.; Patton, M.; Pelton, R. Washing the fibers from foams for higher yields in flotation deinking. Tappi J. 1998, 81 (6), 138–142. (26) Finch, J. A.; Dobby, G. S. Column Flotation; Pergamon Press: New York, 1990. (27) Ajersch, M.; Pelton, R. Mechanisms of pulp loss in flotation deinking. J. Pulp Paper Sci. 1996, 22 (9), 338–345. (28) Zhu, J. Y.; Tan, F. Dynamic drainage of froth with wood fibres. Ind. Eng. Chem. Res. 2005, 44 (9), 3336–3342. (29) Zheng, X.; Franzidis, J.-P.; Johnson, N. W.; Manlapig, E. V. Modelling of entrainment in industrial flotation cells: the effect of solids suspension. Miner. Eng. 2005, 18, 51–58. (30) Zheng, X.; Franzidis, J.-P.; Johnson, N. W. An evaluation of different models of water recovery in flotation. Miner. Eng. 2006, 19, 871– 882.

ReceiVed for reView November 17, 2008 ReVised manuscript receiVed February 2, 2009 Accepted February 11, 2009 IE801753J