**Factor and cluster analyses of the structure of correlations between high consistency pulp properties during refining and paper strength characteristics**,”

*BioResources*18(4), 8090-8103.

#### Abstract

This article analyses high-consistency pulp refining using a disk refiner. During the experiment, the size of the gap between the rotor and stator cutters (0.5 to 1.5 mm), rotor speed (2,000 to 2,500 rpm), pulp consistency (10 to 20%), and freeness value (15 to 60 °SR) of the pulp were varied. The refining results were characterised by changes in 10 output parameters: morphological properties of cellulose fibres (average length, width, fibrillation index, water retention value, average kink angle, and coarseness) and the physical and mechanical characteristics of handsheets (breaking length, bursting strength, tearing resistance, and folding endurance). A total of 56 observations were made on the samples. Factor and cluster analysis methods were used to study the structure of correlations between the output parameters. More than 96% of the total dispersion of all output parameters was due to a change in two latent (hidden) factors: the first one was responsible for 79.6% of the dispersion and is presumably identified as the degree of external fibre fibrillation and the second one (16.6% of the dispersion) as fibre flexibility (including coarseness and average kink angle).

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#### Full Article

**Factor and Cluster Analyses of the Structure of Correlations between High Consistency Pulp Properties during Refining and Paper Strength Characteristics **

Alexander Ushakov,* Yuri Alashkevich, Robert Pen, and Viktor Kozhukhov

This article analyses high-consistency pulp refining using a disk refiner. During the experiment, the size of the gap between the rotor and stator cutters (0.5 to 1.5 mm), rotor speed (2,000 to 2,500 rpm), pulp consistency (10 to 20%), and freeness value (15 to 60 °SR) of the pulp were varied. The refining results were characterised by changes in 10 output parameters: morphological properties of cellulose fibres (average length, width, fibrillation index, water retention value, average kink angle, and coarseness) and the physical and mechanical characteristics of handsheets (breaking length, bursting strength, tearing resistance, and folding endurance). A total of 56 observations were made on the samples. Factor and cluster analysis methods were used to study the structure of correlations between the output parameters. More than 96% of the total dispersion of all output parameters was due to a change in two latent (hidden) factors: the first one was responsible for 79.6% of the dispersion and is presumably identified as the degree of external fibre fibrillation and the second one (16.6% of the dispersion) as fibre flexibility (including coarseness and average kink angle).

*DOI: 10.15376/biores.18.4.8090-8103*

*Keywords: Pulp refining; Correlation factor analysis; Cluster analysis; Morphology of cellulose fibres; Physical and mechanical characteristics of handsheets*

*Contact information: Reshetnev Siberian State University of Science and Technology 31, Krasnoyarskiy Rabochiy Prospekt, Krasnoyarsk, 660037 Russian Federation;*

* * Corresponding author: al.ushakov2194@mail.ru *

**INTRODUCTION**

Pulp refining in disk refiners is an important operation in pulp and paper production on which the morphological properties of fibres and the strength characteristics of paper largely depend (Alashkevich *et al.* 2006, 2010; Chen *et al.* 2016).

There are usually correlations between these characteristics. This indicates the existence of a smaller number of more general, “deep” properties of cellulose fibres that change during refining, which, in turn, results in a change (variance) in the measured characteristics of pulp and paper (Lawley and Maxwell 1962; Pen 1972; Everitt *et al.* 2011; Almonti *et al.* 2019). Such properties are called hidden (latent) factors. They can be identified and analysed by multivariate mathematical statistics, in particular, by the factor and cluster analysis methods (Pen 1972; Kim and Mueller 1986; Strand 1987; Brown *et al.* 2004; Pulkkinen *et al.* 2010; Novoselskaya *et al.* 2019).

In this article, both these methods are used in the analysis of high-consistency pulp refining (from 5% and higher). This research is relevant because fibres during refining can experience various kinds of deformations and structural changes that, when compared to the refining of low-consistency fibrous suspensions, have some differences (Wathén 2006). These structural changes are characterised primarily by such important indicators as: external fibre fibrillation, which increases the outer surface characteristics of fibres and the number of interfibre bonds, as well as internal fibrillation, which is accompanied by an increase in interfibre bonding forces and flexibility and a decrease in fibre coarseness, without weakening the strength of the fibre itself (Matveev 1974; Bhardwaj *et al.* 2004; Hou *et al.* 2011; Chen *et al.* 2017). The listed properties of fibres are largely influenced by the consistency of the refined pulp. Increasing pulp consistency during refining ensures greater external and internal fibre fibrillation, thereby increasing the strength characteristics of the finished paper products (Kang and Paulapuro 2006; Lebedev *et al.* 2018; Przybysz *et al.* 2020; Penkin *et al.* 2022).

A number of studies have shown that a high-consistency pulp refining process is appropriate for obtaining highly-extensible paper, which is especially important in the manufacture of sack papers (Henderson *et al.* 1965; Gurnagul *et al.* 2005). It is also worth noting that high-consistency pulp refining ensures the preservation of the original fibre length due to high interfibre friction and a decrease in the cutting action from the cutting edges due to relatively large gaps between the grinding surfaces of the rotor disks and the refiner stator (Fernando *et al.* 2012; Kerekes 2015; Ushakov *et al.* 2020). This high interfibre friction during high-consistency refining, on the one hand, ensures better fibre processing, giving fibres a high water retention value and an external specific surface area, *i.e.*, indicators characterising changes in internal fibre fibrillation (Sundström *et al.* 1993; Fernando *et al.* 2007, 2011). On the other hand, an excessive increase in pulp consistency reduces fibre fibrillation, causing fibres to twist (Hartler 1995). This deformation is called “fibre latency” (Klark 1983; Gard 2002). When refining high-consistency pulp, fibre latency occurs due to mechanical effects in the refining zone of the disk refiner. This results in a large number of highly deformed (twisted, kinked, or crumpled) fibres in the pulp (Page *et al.* 1985; Pen and Karetnikova 2008).

The purpose of this study is to identify the number and physical nature of hidden factors that cause the dispersion of morphological and paper-forming properties during high-consistency pulp refining.

**EXPERIMENTAL**

**Materials**

Bleached LS ‑1 hardwood sulphate pulp (a semi-finished product from Ilim Group, Bratsk (Russia)) was selected for experimental studies. The degree of delignification (Kappa number) was 2.0 to 4.0. Before refining, the pulp was defibrated with water according to ISO 5263-3 (2004) standard. The refining was carried out in a laboratory disk refiner as presented in Fig. 1.

Pulp of the required consistency was placed into hopper 1 of the disk refiner. After that, screw feeder 2 was used to transfer the pulp from hopper 1 to working area 3 to refine it between the cutters of rotor 4 and stator 5. Next, the pulp was passed through outlet 6. The gap between the rotor and stator cutters was changed using mechanical adjusting device 9 by moving the stator along its axis. The rotational speed of the disk refiner rotor drive and the screw feeder was regulated using SMV frequency converters (AC Technology Corporation, Lenze AC Tech, Uxbridge, MA, USA).

**Fig. 1.** Disk refiner (1 – pulp hopper; 2 – screw feeder; 3 – refining zone; 4 – rotor disk; 5 – stator disk; 6 – outlet; 7 – screw feeder worm gear; 8 – electric motor of disk refiner rotor drive; 9 – mechanical adjusting device)

To assess the variability of the pulp refining quality, an increase in the freeness value was determined according to the Shopper-Riegler method (°SR) using the SR-2 device (Manufacturer Metrotex, Moscow, Russia) as per ISO 5267-1 (2000). For analyses, pulp samples were taken with a freeness value of 15, 30, 45, and 60 °SR. According to ISO 16065-2 (2019), the morphological properties of fibres were determined at least three times for each sample using the *MorFi Neo* fibre analyser (Manufacturer “TECHPAP”, Gieres, France). The studied morphological properties of fibres included such indicators as listed below.

Average fibre length *L _{ avg.}* (mm) was determined according to the Eq. 1,

(1)

where *L _{i}* is the length of developed fibres. As shown in the calculation diagram of Fig. 2,

*L*is determined by the fibre analyser as the sum of segments of rectilinear sections of fibres along their axis;

_{i}*N*is the number of recognised fibres.

**Fig. 2.** Fibre length recognition by fibre analyser

(*L _{i} = F_{A} + F_{B} + F_{C} + …. + F_{H} + … + F_{P}* )

The fibrillation index *Fib* (%) was calculated as the ratio of the sum of the lengths of all fibrils to that of the lengths of all recognised fibres and can be expressed through the Eq. 2,

(2)

where *Fi* is the ‑sum of all fibrils per fibre, and *L _{i}* is the length of developed fibres.

Fibre coarseness *k* (mg/m) is calculated as the ratio of the mass of all fibres (recognised by the fibre analyser) to their total length. Average fibre width *Z* (µm), as well as average fibre length, is summarily calculated using the device for each fibre segment. Average kink angle *A* (°), is determined as the points of abrupt change in the direction of the fibres where they can break.

In addition to the listed morphological properties of the fibres, the water retention value (WRV) was evaluated as an indicator characterising the fibre swelling degree according to ISO 23714 (2014). The WRV of the pulp indicates the moisture remaining in it after centrifugation under certain conditions. Pulp centrifugation was completed using the MPW – 310 device (MPW Instruments, Warsaw, Poland). The moisture content of the pulp after centrifugation was determined by the difference in the mass of the sample before and after drying (%), and can be expressed using the Eq. 3,

(3)

where *W*_{wet} is the mass of wet fibres after centrifugation (g), and *W*_{dry} is the ‑mass of dry fibres (g).

To determine the physical and mechanical characteristics, a sheet machine (Werkstoffprufmaschinen, Leipzig, Germany) was used to form handsheets. Before testing the physical and mechanical characteristics, the handsheets were conditioned under standard conditions. The physical and mechanical characteristics of the handsheets were evaluated according to the following indicators:

- Breaking length in accordance with ISO 1924-2 (2008), using a RMB 30M tensile testing machine (Experimental Production Workshop, Moscow, Russia);
- Bursting strength in accordance with ISO 2758 (2014), using an EC35 apparatus (TMI 13-6, Rotterdam, Holland);
- Tearing resistance in accordance with ISO 1974 (2012), using a RB-1 device (Experimental Production Workshop, Moscow, Russia);
- Folding endurance in accordance with ISO 5626 (1993), using the DRK111B Folding Tester (Shandong Drick Instruments Co., Ltd., Jinan, China)

**Methods**

*Pulp refining and factor and cluster analyses*

During the experiment, the size of the gap between the rotor and stator cutters (with a range of variation 0.5 to 1.5 mm), rotor speed (2,000 to 2,500 rpm), pulp consistency (10 to 20%), and freeness value (15 to 60 °SR) of the pulp were varied. Table 1 presents the input technological factors of the refining process and the output parameters of the morphological properties of the pulp and the physical and mechanical characteristics of the handsheets. A total of 56 observations (refining modes) were made on the samples. The observations and their statistical characteristics are given in the Appendix (Tables S1 and S2).

The results (statistical characteristics, correlation, factor, and cluster analyses) were mathematically processed using the Statgraphics Centurion XVI software product (free version).

**Table 1.** Factors of the Refining Process and Output Parameters

**RESULTS AND DISCUSSION**

The preliminary statistical analysis of the observations revealed correlations between most of the output parameters (Table 2). This is a consequence of a relatively small number of common properties – “hidden” (latent) factors (*common factor*, *latent factor*) *f _{ j}* that exert a greater or lesser influence on the output parameters and determine the structure of the correlation matrix.

**Table 2.** Correlation

This study used *factor analysis* and *cluster analysis* to identify the number and nature of hidden factors [1 through 5].

Factor analysis was used to derive a regression equation based on a matrix of correlations between output parameters. Linear regression is written as Eq. 4,

(4)

where *f _{ j}* is the hidden factor

*“common (latent) factor”*;

*t*is the number of latent factors;

*m*is the number of output parameters (in the studied case,

*m*= 10);

*l*is the loading of the

_{ it}*j*

^{th}latent factor on the

*i*

^{th}output parameter;

*ε*represents the residuals representing the sources of deviations affecting only

_{i}*Y*. Equation 4 expresses the basic hypothesis of factor analysis: the set of correlated variables

_{ i}*Y*1, 2, …,

_{i}(i =*m)*can be represented as a linear function of a smaller number of latent factors

*f*1, 2, …,

_{ j}(j =*t)*and a set of independent residuals ε

_{i}_{.}

Factor analysis of the results given in Table S1 was performed by the Minres method. The *Varimax Rotation* criterion was used for orthogonal transformation of factor loadings. Statistical significance with a confidence of at least 95% was established for two latent factors responsible for 96.19% of the total dispersion of all 10 output parameters, including 79.56% of the dispersion for the first factor and 16.62% for the second one (Table 3).

**Table 3.** Factor Loading Matrix after the Varimax Rotation

Figure 3 shows a two-dimensional factor space with the output parameters under observation. The coordinates of the points are *factor loadings* (see Table 3).

In addition to factor analysis, cluster analysis of the output parameters was performed using the *Ward’s, Distance Metric Squared Euclidean* method (Fig. 4).

The classification procedures used are based on different data grouping methods. The object of factor analysis is the matrix of paired linear correlations between the output parameters. In cluster analysis, the basis for grouping is the geometric distances between the normalised values of the output parameters. Nevertheless, the results of the groupings turned out to be identical. This is confirmed by a visual comparison of Figs. 3 and 4.

**Fig. 3.** Plot of the factor loading

**Fig. 4.** Results of clustering by fibre properties

The main part of the output parameters (_{Y2, Y4}‑, Y5, Y7, Y10) was grouped into a relatively dense cluster on the positive part of the coordinate axis of the first latent factor (Fig. 3). The nature of this factor can be identified with the external fibre fibrillation degree: the positive correlation of this property with the water retention value of the pulp, the fibrillation index, and the strength characteristics of the handsheets did not contradict the generally accepted prior information.

The negative correlation between the average fibre length *Y _{1 }*and other characteristics in the studied cluster was unexpected. A possible reason is because of a decrease in the length of the fibres during refining with a simultaneous increase in the external fibrillation degree. Figure 5 shows the relationship between these properties for one of the refining modes. Similar dependences are revealed in other refining modes within the pulp consistency range of 10 to 20%.

The second latent factor affects the coarseness of the fibres *Y*_{ 3} and their average kink angle *Y _{6}*. Presumably, the nature of this factor is associated with internal fibrillation. High-consistency pulp refining is accompanied by an increase in internal fibrillation, resulting in increased flexibility and plasticity. The increased flexibility is accompanied by an increase in the number of kinked fibres and a decrease in their coarseness, as shown in Fig. 6.

**Fig. 5.** The relationship between average fibre length on the fibrillation index (refining mode: rotor speed 2,000 rpm; gap between the rotor and stator cutters 1.5 mm; pulp consistency 10, 15, and 20%)

**Fig. 6.** The relationship between average kinked angle of fibres on their coarseness (refining mode: rotor speed 2,000 rpm; gap between the rotor and stator cutters 1.5 mm; pulp consistency 10, 15, and 20%)

**CONCLUSIONS**

- The study conducted between the morphological properties of the fibers and the strength characteristics of the paper by the methods of factor and cluster analysis showed that the share of the total dispersion of the studied parameters of the refining process is determined by two hidden factors. One of the factors is related to the degree of fibrillation of the fibers, and the other to their flexibility. The total share of the total variance of all observed indicators, due to the influence of two hidden factors, is 96.2% of their total variance. The first of the identified factors determines 79.6% of the variance of the variance in the observed indicators, the second 16.6%.
- The effectiveness of “information extraction” by multivariate mathematical statistics (correlation, factor, and cluster analysis methods) was demonstrated using the example of studying experimental data on the pulp refining process, which is one of the most important production processes in paper technology. It was established that the external fibrillation of cellulose fibres makes a major contribution to the variability of the physical and mechanical properties of paper sheets during high-consistency pulp refining.

**ACKNOWLEDGMENTS**

This work was carried out under the State Assignment issued by the Ministry of Education and Science of Russia for the project: “Technology and Equipment for the Plant Biomass Chemical Processing” by the Plant Material Deep Conversion Laboratory (Subject No. FEFE-2020-0016).

This work was performed using equipment of the Centre for Collective Use of the Krasnoyarsk Research Centre of the Siberian Branch of the Russian Academy of Sciences. We express gratitude to the staff of this centre for their assistance in our research.

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Article submitted: July 8, 2023; Peer review completed: July 29, 2023; Revised version received: October 3, 2023; Published: October 12, 2023.

DOI: 10.15376/biores.18.4.8090-8103