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Nordic Pulp & Paper Research Journal

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Volume 33, Issue 1

Issues

Optimum strategies for pulp fractions refining

Patrick Huber / Bruno Carré / Saurabh Kumar / Michael Lecourt
  • FCBA, Pôle technologique IntechFibres, Domaine universitaire CS 90251, 38044 Grenoble Cedex 9, France
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2018-05-23 | DOI: https://doi.org/10.1515/npprj-2018-3012

Abstract

Separate refining of pulp fractions before remixing has sometimes been compared to whole pulp refining, with no definitive answer about the interest of doing so. In this work, we present a general method to help decide whether fractions refining can be profitable or not. Recommendations for fractions refining strategies are given, depending on the evolution of pulp properties as a function of applied energy. In the tested case (bleach kraft pulp mix (75 % eucalyptus/25 % radiata pine) fractionated on a 2-stage hydrocyclone process), optimised fractions refining provided a gain of about 40 kWh/T compared to whole pulp mix refining, when targeting a tensile index of 50 N.m/g.

Keywords: energy; fractionation; optimisation; refining; tensile

Introduction

Fractionation has been proposed prior to refining, as a solution for applying dedicated refining treatment to each fraction. Some studies reported significant energy gain compared to mixed refining at given properties, while others concluded that fractions refining was not worth it. The reasons for success or failure were not clearly established.

Refining is an energy-intensive unit operation which can represent from 5 up to 30 % of the total energy requirements of the papermaking process, depending on considered paper grades (Suhr et al. 2015). Refining conditions are adapted to fibre furnish (short or long fibres), in order to develop performances in the most efficient and beneficial way. Hence, separate refining is recommended whenever possible (Baker 2005). Another solution for refining homogenous fibres is fractionation. It opens way to apply dedicated refining conditions to each fraction, based on chosen parameter, such as fibre size, coarseness, etc. However, it is not clear what the optimum refining strategies should be, and whether the fractionation/refining process can offer energy savings or performances enhancement.

Fractionation separates fibres into several pulp streams, based on chosen criteria. The two main fractionation technologies are based on screens, with slots or holes, and hydrocyclone. Screen fractionation allows to separate fibres depending on their length (Gooding et al. 2004, Qazi et al. 2015) whereas hydrocyclone fractionation allows to separate fibres depending on their development (related to following parameters: wall thickness, density, stiffness, flexibility, fibrillation), resulting from their different migration behavior in the centrifugal flow field (Vomhoff and Grundström 2003, Asikainen et al. 2010, Julien Saint Amand and Perrin 2003).

Having different fractions makes it possible to apply the right treatment to the right fraction. In recycled pulp stock preparation, fractionation allows to generate a fraction concentrated in dirt particles and to apply a dispersing treatment only to that fraction. Fractionation is also proposed in deinking lines to concentrate ink and filler particles into one fraction and floating only this fraction, with a total rethinking of the deinking process (Carré et al. 2012, Kumar 2012, Kumar et al. 2015). Fractionation can also be proposed for selective bleaching (e. g. in TMP, where fines fraction contain most of the chromophores (Franzen 1982, Petit-Conil and Laurent 2003)). Finally, selective refining of pulp fractions can be applied in chemical pulps (El-Sharkawy et al. 2008a, 2008b, Koskenhely et al. 2005a).

Generated fractions may also be used as additives for enhancing the properties of other pulps (El-Sharkawy et al. 2008b, Koskenhely et al. 2005b, Moller et al. 1979).

Refining is a mandatory operation in most mills using kraft fibres. It develops fibres bonding potential, impacts their morphology and enhances paper sheet formation. As an energy intensive technology, several solutions for reducing energy consumption were developed. These include improvement of refiner technology (plate designs, refiner type, etc.). Alternative treatment of the fibre suspension has been proposed as well. Some chemicals exist to improve fibre swelling before refining (Milichovsky 1990). Alkaline pH and counter ions can also have an impact on fibre behavior (Mohlin 2002) and especially swelling. Other solutions are based on use of enzymes (Lecourt et al. 2010). In this case, cellulase showed the most efficient way to reduce energy consumption. Fibre furnish selection is another way to reduce energy consumption during refining. The most representative situation is eucalyptus. Indeed, for selected origins, this fibre presents a high refinability, requiring less energy for reaching a high tensile compared to softwood for example. Nevertheless, other performances are affected and require adapted conditions.

Fractionation/refining studies have been reported several times, however such strategy is rarely used in the industry. Among the various studies reporting the interest or not of such an approach, (Vomhoff and Grundström, 2003) showed that hydrocyclone fractionation of NBSK pulp lead to fractions with very different refining ability. If the coarse fraction needed more energy to achieve a certain °SR, the fine fraction required much less. In this paper, there was however no information on the interest of fractionation/refining since there was no remixing of the different fractions after refining and no data concerning the possible refining energy gain. (Koskenhely et al. 2005a) did an extensive study to understand how bleached softwood chemical pulp coarse and fine fractions obtained by screen and hydrocyclone fractionations should be refined. Different types of refining mechanisms have been proposed depending on fractions and specific edge load: coarse fraction for example was again identified as requiring more energy for a given strength. However, again, no remixing of the fractions after refining was performed, so that evaluation of possible energy gains was not possible. (El-Sharkawy et al. 2008a, 2008b) also studied the interest of fractionation refining, with softwood and eucalyptus, fractionated by screening. Experiments showed that selectively refining the reject instead of the whole pulp lead to an improved tear/drainage/refining energy compromise. (Asikainen 2013, Asikainen et al. 2010) studied birch and softwood pulps fractionation refining, fractionation being done by screens or by hydrocyclones. Birch fractions were proposed to be used as reinforcement pulps in fine papers and board. Birch coarse fraction was recommended to be used on the top layer whereas birch fine fraction was proposed to increase internal bonding. Softwood fractions were proposed as reinforcement pulp, as their separate refining improves the tear/drainage compromise.

More recently, a Campo (2015) tried to understand when fractionation/refining was of interest, using data from Vomhoff and Grundström (2003). Thanks to a mathematical analysis of the tensile/refining energy curves of different fractions, he concluded that potential gains are small and limit the interest of fractionation/refining. On the other hand, for recycled board processes, Musselmann (1983) reported energy saving of 25 % by optimizing refining conditions of short and long fibre fractions.

The objective of this paper is to answer the two following questions. When is it profitable to apply dedicated treatment to generated fractions, to reach a given target property after remixing? What should be the optimal refining strategy to apply for each fraction? We illustrate the methods with the example of fractions refining to develop tensile index.

Materials and methods

Pulps

The tested pulp was a mix of 75 % eucalyptus/25 % radiata pine, corresponding to a typical furnish for wood free copy paper. The pulp was slushed in a low consistency pulper (5 % consistency, 30 min, 45 °C). The pulp had an initial drainage index of 17 °SR.

Schematic and conditions of the fractionation process (mass flows are reported in bold face).
Figure 1

Schematic and conditions of the fractionation process (mass flows are reported in bold face).

Fractionation

A 2-stage feed forward fractionation by hydrocyclone (batch) was adopted. The pilot trials were done with an 80 mm head diameter industrial fractionating hydrocyclone (NOSS AM80A). Conditions are described in Figure 1. The two stage feed forward fractionation was performed batch wise; with the same single hydrocyclone being used for both the stages. Due to limited storage capacity, the 1st stage hydrocyclone base fraction (or the accepts) were thickened on the pilot vacuum filter. The filter offers high fibre and fines retention. This thickened base fraction was added to the 2nd stage base fraction to get a combined fraction and then thickened on the same vacuum filter. This thickening was necessary for the subsequent refining operations.

The properties of the fractions relevant for the study (fine content, macrofibrillation index, mean fibre coarseness) were measured with a MORFI fibre analyser (Techpap, France) (Eymin-Petot-Tourtollet 2000).

Schematic view of the refining installation.
Figure 2

Schematic view of the refining installation.

Refining

The feed pulp, the accepts and the rejects were refined separately, using same conditions.

A 12 single disc refiner was used. Installation was equipped bytwo tanks and conveying pumps (Figure 2). Pulp was introduced and diluted down to 4.5 % consistency in tank 1. Suspension was sent through the refiner by pump 1 with a flow fixed at 5 m3/h. Motor load was adapted to the fixed target by adjusting plate gap. Target was defined by the refining intensity to be applied. Pulp was recovered in tank 2. Refining ended when tank 1 was emptied.

This protocol made it possible to consider one refining stage for all the suspension. For next refining stage, pump 1 was stopped and pump 2 switched on to fill in tank 1.

Once filled in, another refining stage could be performed. The refining conditions applied and plates used were adapted for reaching a refining intensity of 0.8 Ws/m and 4 refining stages. Energy applied was calculated by dividing net power applied (kW) by mass flow (dry T/h). Plate design was selected in order to be compatible with the refining conditions fixed for the trials. Plate design is function of the type of refiner as power and RPM. Power was calculated based on the plate cutting length at 1500 rpm, given by the plate producer.

Handsheet preparation and testing

Handsheets were produced on a Formette Dynamique laboratory sheet former (Techpap, France), with jet speed/wire speed = 0.652, so that the fibres are oriented in the machine direction. Handsheets were all manufactured with a 80 g/m² grammage. In order to obtain a good retention of fines, a conventional retention aid was added (cationic polyacrylamide, FENNOPOL K3400R from Kemira, 0.5 kg/T). Handsheets were then pressed on a roll press with linear load = 5 kN/m (Techpap, France) and dried for 10 min at 105 °C on a plate dryer (Techpap, France).

The sheet physical properties have been assessed using the following standard methods: pre-conditioning (NF EN 20 187, 1993), basis weight (NF EN ISO 536, 1996), tensile properties (ISO 1924-2). The reported tensile index value is the geometrical average of machine- and cross-direction values.

Analysis

We determine the optimum treatment for each fraction to reach target property after remixing the fractions, and compare with the energy requirements for the whole pulp treatment. We assume that the considered pulp property is additive (so that it can be predicted from mixture rules). Also we suppose that the entirety of fractions is used (so that no losses are generated). We consider refining as the dedicated treatment (Figure 3).

Comparison of the classical process (refining of the whole pulp flow) and the fractionated process (generation of 2 fractions, dedicated refining applied to each fraction, then remixing of the fractions).
Figure 3

Comparison of the classical process (refining of the whole pulp flow) and the fractionated process (generation of 2 fractions, dedicated refining applied to each fraction, then remixing of the fractions).

We suppose that evolution of the tensile index of feed pulp, accepts and rejects fractions as a function of the energy applied during refining, defined as refining curve, can be described as follows: Feed (f):Tf=T0f+TmfT0fkfRf1+kfRf(1)Accepts (a):Ta=T0a+TmaT0akaRa1+kaRa(2)Rejects (r):Tr=T0r+TmrT0rkrRr1+krRr(3) where R is the specific energy consumption (kWh/ton), T is the corresponding tensile index, and T0 (N.m/g), Tm (N./g) and k (ton/(kWh)) are parameters that describe the initial value, the plateau value and the curvature of the refining curve respectively (see Nomenclature section).

The proposed model is purely empirical and has been found to provide an acceptable fit to a large set of refining data. The form of the chosen model does not preclude the general applicability of the results.

The constraint to meet the target tensile Tg, after remixing the refined fractions, is expressed as: pTa+1pTr=Tg(4) where p is the accepts mass flow rate.

This sets the link between the refining energy to be applied to the accepts (Ra) and the rejects (Rr) fractions: Rr=[kapRaTma+kaRa1Tg+kakapRap+1T0r+pT0a]×[kakrpkakrRa+krpkrTmrkakrpRaTma+kakrRa+krTgkrpT0a]1(5)

The total refining energy applied to the fractions to minimise is: R=pRa+1pRr(6) The total refining energy R depends on Ra and Rr. As Ra and Rr are linked through the target tensile condition, the minimum total refining energy can be calculated for instance by dRdRa=0, so that: Raˍmin=p1Δ+krkrpTmrkrTg+krpT0akakrp1TmrpTma+Tg,(7) where: Δ=kakrTmaT0aTmrT0r

Replacing in the total refining energy expression, finally gives the expression of the minimum refining energy for the fractionation refining Rmin=[(2p22p)Δ+(krpkrp2)Tmr+(kapkap2)Tma+kakrpkaTg+(kap22kap+ka)T0r+krp2T0a]×[kakrp1TmrpTma+Tg]1(8)

The refining energy to be applied to the feed pulp to meet the target tensile is: Rf=TgT0fkfTmfkfTg(9) The gain from fractionation refining is G=RfRmin(10)

We study in which conditions G may be positive or negative.

If all refining curves are parallel, the slopes of the refining curves are equal for a given refining energy. This implies that both fractions behave similarly during refining. Therefore the same refining energy should be applied to both fractions (Raˍmin=Rrˍmin). The limit condition where fractionation refining is equivalent to mixed refining occurs when the point corresponding to the remixed refined fractions coincides with the point of the refined feed pulp. Thus, the null gain situation is given by 1pTr+pTa=Tf. Therefore the gain from fractionation refining is positive whenever pTf(R)Tr(R)Ta(R)Tr(R), independently of Tg. As the refining curves are parallel, we have for instance pT0fT0rT0aT0r. In other words, fractions refining becomes advantageous when accepts fraction with mass flow p, generates a property difference greater than (1p) with respect to feed pulp (Figure 4).

Example of optimum fractions refining when all refining curves are parallel, limit condition for null gain (p = 0.4, Tg{T_{g}} = 45 N.m/g).
Figure 4

Example of optimum fractions refining when all refining curves are parallel, limit condition for null gain (p = 0.4, Tg = 45 N.m/g).

In the general case, where refining curves may have any shape, the null gain condition is obtained when the optimum refining points for the 2 fractions are aligned with the target point for the entire pulp. This alignment condition is set by RaˍminRrˍminRrˍminRf=TaˍminTrˍminTrˍminTg(11)

As tensile and refining are linked by the refining curves, we have: RaˍminRrˍminRrˍminRf=1p(12) where p is the critical accept rate that makes fractions refining just profitable. The full expression of p is too long to be detailed here (see Supplementay material). Note that here p’ depends on Tg. In the following example (Figure 5), the fractionation refining becomes profitable when p > 0.315, for given fractions properties and tensile target after remixing. In practice, the fractions properties and the mass reject rate are not independent. The critical p value, however, gives a practical assessment of the potential profitability of the fractionation/refining processes for a given target tensile index.

Example of optimum fractions refining in the general case (p is variable, Tg{T_{g}} = 45 N.m/g).
Figure 5

Example of optimum fractions refining in the general case (p is variable, Tg = 45 N.m/g).

We now set the p value, and define general guidelines for fractions refining strategies. Shall we spend more energy on the accepts or the rejects fractions? The general answer is to refine more the fraction that is more responsive to refining. Whatever the curvature of the refining curves, there exists a refining energy where the derivatives of the refining curves of both fractions are equal. This corresponds to a critical target tensile after remixing the fractions (Tg). The full analytical expression of Tg is given as Supplementary material. To define the optimum fractions refining strategies, we distinguish 2 cases. When the curvature of the refining curve of the accepts fraction is larger than that of the rejects (ka>kr) the slope of the refining curve for the accepts is larger than that of the rejects below Tg, and vice-versa above Tg. Thus, the optimum refining strategies consists in spending more energy on the accepts than on the rejects below Tg, and vice-versa above Tg (Figure 6). When (ka<kr), the optimum refining strategy is opposite: refine more the rejects below Tg, and refine more the accepts above Tg (Figure 7).

Optimum refining strategies for the fractions when ka>kr{k_{a}}>{k_{r}} (p = 0.3, Tg{T_{g}} is variable).
Figure 6

Optimum refining strategies for the fractions when ka>kr (p = 0.3, Tg is variable).

Optimum refining strategies for the fractions when ka<kr{k_{a}}<{k_{r}} (p = 0.4, Tg{T_{g}} is variable).
Figure 7

Optimum refining strategies for the fractions when ka<kr (p = 0.4, Tg is variable).

Relative variation of fractions properties relevant to fibre development (MORFI fibre analyser).
Figure 8

Relative variation of fractions properties relevant to fibre development (MORFI fibre analyser).

Test of tensile index mixture rule (comparison of measured values of tensile index for several mixtures of fractions and comparisons with values calculated from a linear mixture rule).
Figure 9

Test of tensile index mixture rule (comparison of measured values of tensile index for several mixtures of fractions and comparisons with values calculated from a linear mixture rule).

Results

The efficiency of the fractionation process is illustrated in Figure 8. The accepts are concentrated in fine elements, fibrillated and have low coarseness fibres.

The additivity of the tensile index property was tested by mixing various refined fractions according to the fractionation mass split, and comparing with the prediction from the linear mixture rule (Figure 9). A good agreement was generally observed. In a few cases, the calculated tensile was slightly lower than the measured tensile. Therefore, model predictions provide a conservative estimate of the refining energy to be applied to the fractions for a given target tensile index after remixing. It has been shown that the tensile of hardwood and softwood pulp mixtures is roughly linearly additive (Chauhan et al. 2013).

We now apply the proposed optimisation method to our case. Pulp fractions exhibit different refining behavior, with the accepts being more sensitive to refining than the rejects (Figure 10). Tensile index development was faster in the case of accepts compared to others. Indeed, such fibres were more amenable to modification during refining, namely hydration, fibrillation and cutting. On the contrary, rejects presented coarser elements requiring more energy for reaching similar fibre bonding potential and consequently, tensile index.

Refining curves of the feed pulp and the fractions, and example of dedicated fractions refining (when targeting a tensile index = 50 Nm/g, optimisation of fractions refining conditions can yield energy savings of 41.9 kWh/T after remixing the fractions, compared to refining the whole pulp flow).
Figure 10

Refining curves of the feed pulp and the fractions, and example of dedicated fractions refining (when targeting a tensile index = 50 Nm/g, optimisation of fractions refining conditions can yield energy savings of 41.9 kWh/T after remixing the fractions, compared to refining the whole pulp flow).

Potential refining energy savings from fractions refining as a function of target tensile index after remixing the fractions.
Figure 11

Potential refining energy savings from fractions refining as a function of target tensile index after remixing the fractions.

The proposed empirical model provides an acceptable fit of the refining curves of both fractions and feed pulp. For a target tensile index Tg = 50 Nm/g, the optimum fractions refining is given by Ra,min = 179.9 kWh/T and Rr,min = 169.9 kWh/T. With p = 0.526, this yields a total refining energy for the fractions Rmin = 175.1 kWh/T, to be compared to the whole pulp refining energy Rf,min = 217.0 kWh/T. In this case the gain from fractions refining is +41.9 kWh/T. The critical tensile index Tg is 55.74 Nm/g, hence Tg<Tg. As we have ka>kr, this indicates that more refining energy should be spent of the accepts than on the rejects indeed (Ra,min>Rr,min).

The critical mass accepts rate for profitability calculated from the fitted refining curve is p = 0.396 in this case. Therefore with p>p in our case, the fractionation/refining process must be profitable.

The expected gain from the fractionation/refining process depends on the tensile aimed at. The absolute gain increases up to Tg = 50.64 Nm/g, then sharply decreases (Figure 11). Above Tg = 57.98 Nm/g, the fractionation-/refining process is not profitable anymore, as the gain becomes negative. As a matter of fact, the relative gain is maximum for low target tensile, then decreases with target tensile.

Optimum refining strategies for the fractions as a function of target tensile index after remixing the fractions.
Figure 12

Optimum refining strategies for the fractions as a function of target tensile index after remixing the fractions.

The optimum refining strategy is illustrated in Figure 12. It shows that more refining energy should be spent on the accepts for low target tensile index, up to Tg = 55.74 Nm/g. Above that critical target tensile index, we have (Ra,min<Rr,min).

Discussion

In the tested case, the fractionation/refining process was profitable up to a maximum tensile index. Then, we demonstrate that above a certain value, initial whole pulp refining, without fractionation, is more energy efficient. Consequently, the interest for fractionation prior to refining depends on the refining sensitivity of the fractions and the fractionation mass split. In some cases, fractionation/refining may not be interesting at all, whatever the target tensile index. That explains previous literature results which were sometimes in favour or against the fractionation/refining process. Therefore, we do not advocate for fractionation and dedicated refining in general, but provide methods to identify conditions when implementation is profitable. The potential operating gain will help deciding whether it is worth investing in the technology or not. Admittedly, our approach does not account for investment costs yet. The optimised refining process will call for additional investment (fractionation + thickening stage + refiner on one or both fractions depending on the refining target) but this will be balanced by a lower energy applied during refining, and especially a higher drainage ability on the PM reducing both wet end chemicals and steam consumption during drying.

Also note that the refining conditions were identical for all fractions. Refiner segment selection was made according to 2 parameters: the possibility to reach chosen SEL and allowing regular pulp flow, without any plugging. This was a good compromise for all the fibre grades investigated. Dedicated refining conditions for each fraction may lead to further improvement.

The proposed methods offer general guidelines for refining strategies. Usually, the accepts fraction (which contains more fine elements) has a better response to refining (ka>kr), so that more refining energy should be spent to refine it, when targeting moderate target tensile index. However in some unusual cases (as with radiata pine pulp for instance) the rejects (containing more coarse and rigid fibres) respond better to refining in the range of low applied energy with respect to tensile index development (i. e. the curvature of their refining curve is higher). Therefore, the optimal refining strategy consists in refining more the rejects than the accepts in this particular case.

The proposed empirical model for describing tensile index evolution with refining energy applied was versatile enough to fit with several types of pulp. Any other property that follows a similar concave curve could be described, and therefore optimised using the proposed methods. However, the model is not applicable to convex curves, as would be the increase of °SR as a function of refining energy.

We proposed to use an analytical optimisation scheme, in order to better understand the optimum refining strategies and provide as general answers as possible. The identified optimum refining strategies may apply to any monotonically increasing concave property. In some cases, with more than two available fractions, it may be easier to describe refining curves with piece-wise linear functions for instance, and resort to numerical optimisation.

Admittedly, the proposed methods have several constraints. The model requires refining curves and fractionation mass split to calculate the potential gain as a function of target tensile index. In order to estimate how far we are from the null gain situation (compared to whole pulp refining), we calculate the critical accepts mass flow, at constant fractions properties. However fractions properties and mass flows are not independent, as varying the fractionation mass split will alter the properties of the fractions. This hypothesis does not undermine the prediction of the potential gain, but may limit the concept of critical accepts mass flow. Secondly, the analysis is focused on tensile index development and does not account for the corresponding pulp drainage penalty. It may be desirable to optimise not only a given mechanical property, but a compromise between a mechanical property and drainage. This may change the optimum fractions refining strategy. In addition, refining conditions could be changed depending on the fibre furnish, increasing the energy savings through dedicated optimization.

The proposed method could also be used to optimise refining operations for mills which refine separately two given pulp streams (without fractionation), before remixing.

Conclusions

We proposed general method to assess the interest for separate refining of pulp fractions, compared to whole pulp refining. The potential gain from fractions refining can be calculated from refining curves and fractionation mass split for a targeted tensile index. A critical accepts mass flow measures how far the given conditions are from the null gain situation. The model predicts the conditions which make fractions refining profitable or not.

Experimental trials, considering a pulp furnish (75 % BEKP/25 % radiata pine) fractionated by a 2-stage hydrocyclone process, show that refining of fractions provides a gain of about 40 kWh/T compared to whole pulp mix refining, when targeting a tensile index of 50 N.m/g and keeping constant the refining conditions.

General recommendations for fractions refining strategy can be formulated. The main governing parameter is the curvature of the fractions refining curves presenting the property investigated as a function of the energy consumption. Besides, the fractionation mass split is of critical importance. In the most likely case where the accepts show a better response to refining than the rejects, more refining energy should be spent on the accepts than on the rejects, up to a certain critical target tensile index. Above that critical tensile index, the rejects should be more refined than the accepts.

The same method can be applied to other treatments developing a selected property (dedicated bleaching to develop brightness, dedicated flotation to remove ink, etc.), provided that the descriptive trends have similar shape and the property follows mixture rules.

Nomenclature

Tf

tensile index of feed pulp

T0f

initial tensile index of feed pulp

Tmf

plateau value of tensile index of feed pulp

kf

curvature of the refining curve for feed pulp

Rf

refining energy applied to feed pulp

Ta

tensile index of accepts

T0a

initial tensile index of accepts

Tma

plateau value of tensile index of accepts

ka

curvature of the refining curve for accepts

Ra

refining energy applied to accepts

Tr

tensile index of rejects

T0r

initial tensile index of rejects

Tmr

plateau value of tensile index of rejects

kr

curvature of the refining curve for rejects

Rr

refining energy applied to rejects

p

accepts mass flow rate

Tg

target tensile

G

gain from fractionation refining

Rmin

minimum refining energy for the fractionation refining

Acknowledgments

Frédérique Entressangle, Pascal de Luca, Adrien Soranzo are thanked for experimental work.

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Supplemental Material

The online version of this article offers supplementary material (https://doi.org/10.1515/npprj-2018-3012).

Full analytical expressions of relevant quantities (Raˍmin, Rrˍmin, Rmin, Rfˍmin, G, p, Tg) can be obtained from the authors.

About the article

Received: 2017-08-30

Accepted: 2017-12-20

Published Online: 2018-05-23

Published in Print: 2018-05-23


This work was supported by CTP and CTPi members.


Conflict of interest: The authors do not have any conflicts of interest to declare.


Citation Information: Nordic Pulp & Paper Research Journal, Volume 33, Issue 1, Pages 3–11, ISSN (Online) 2000-0669, ISSN (Print) 0283-2631, DOI: https://doi.org/10.1515/npprj-2018-3012.

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